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This **glossary of engineering terms** is a list of definitions about the major concepts of **engineering**. Please see the bottom of the page for glossaries of specific fields of engineering.

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**Absolute electrode potential**- In electrochemistry, according to an IUPAC definition,
^{[1]}is the electrode potential of a metal measured with respect to a universal reference system (without any additional metal–solution interface). **Absolute pressure**- Is zero-referenced against a perfect vacuum, using an absolute scale, so it is equal to gauge pressure plus atmospheric pressure.
**Absolute zero**- Is the lower limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as 0. Absolute zero is the point at which the fundamental particles of nature have minimal vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion. The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as −273.15° on the Celsius scale (International System of Units),
^{[2]}^{[3]}which equals −459.67° on the Fahrenheit scale (United States customary units or Imperial units).^{[4]}The corresponding Kelvin and Rankine temperature scales set their zero points at absolute zero by definition. **Absorbance**- Absorbance or
*decadic absorbance*is the*common logarithm*of the ratio of incident to*transmitted*radiant power through a material, and*spectral absorbance*or*spectral decadic absorbance*is the common logarithm of the ratio of incident to*transmitted*spectral radiant power through a material.^{[5]} **AC power**- Electric power delivered by alternating current; common household power is AC.
**Acceleration**- The rate at which the velocity of a body changes with time, and the direction in which that change is acting.
**Acid**- A molecule or ion capable of donating a hydron (proton or hydrogen ion H
^{+}), or, alternatively, capable of forming a covalent bond with an electron pair (a Lewis acid).^{[6]} **Acid–base reaction**- A chemical reaction that occurs between an acid and a base, which can be used to determine pH.
**Acid strength**- In strong acids, most of the molecules give up a hydrogen ion and become ionized.
**Acoustics**- The scientific study of sound.
**Activated sludge**- A type of wastewater treatment process for treating sewage or industrial wastewaters using aeration and a biological floc composed of bacteria and protozoa.
**Activated sludge model**- A generic name for a group of mathematical methods to model activated sludge systems.
**Active transport**- In cellular biology, active transport is the movement of molecules across a membrane from a region of their lower concentration to a region of their higher concentration—against the concentration gradient. Active transport requires cellular energy to achieve this movement. There are two types of active transport:
*primary active transport*that uses ATP, and*secondary active transport*that uses an electrochemical gradient. An example of active transport in human physiology is the uptake of glucose in the intestines. **Actuator**- A device that accepts 2 inputs (control signal, energy source) and outputs kinetic energy in the form of physical movement (linear, rotary, or oscillatory). The control signal input specifies which motion should be taken. The energy source input is typically either an electric current, hydraulic pressure, or pneumatic pressure. An actuator can be the final element of a control loop
**Adenosine triphosphate**- A complex organic chemical that provides energy to drive many processes in living cells, e.g. muscle contraction, nerve impulse propagation, chemical synthesis. Found in all forms of life, ATP is often referred to as the "molecular unit of currency" of intracellular energy transfer.
^{[7]} **Adhesion**- The tendency of dissimilar particles or surfaces to cling to one another (cohesion refers to the tendency of similar or identical particles/surfaces to cling to one another).
**Adiabatic process**- A process where no heat energy is lost to outside space.
**Adiabatic wall**- A barrier through which heat energy cannot pass.
**Aerobic digestion**- A process in sewage treatment designed to reduce the volume of sewage sludge and make it suitable
^{[8]}for subsequent use.^{[9]} **Aerodynamics**- The study of the motion of air, particularly its interaction with a solid object, such as an airplane wing. It is a sub-field of fluid dynamics and gas dynamics, and many aspects of aerodynamics theory are common to these fields..
**Aerospace engineering**- Is the primary field of engineering concerned with the development of aircraft and spacecraft.
^{[10]}It has two major and overlapping branches: Aeronautical engineering and Astronautical Engineering. Avionics engineering is similar, but deals with the electronics side of aerospace engineering. **Afocal system**- An optical system that produces no net convergence or divergence of the beam, i.e. has an infinite effective focal length.
^{[11]} **Agricultural engineering**- The profession of designing machinery, processes, and systems for use in agriculture.
**Albedo**- A measure of the fraction of light reflected from an astronomical body or other object.
**Alkane**- An alkane, or
*paraffin*(a historical name that also has other meanings), is an acyclic saturated hydrocarbon. In other words, an alkane consists of hydrogen and carbon atoms arranged in a tree structure in which all the carbon–carbon bonds are single.^{[12]} **Alkene**- An unsaturated hydrocarbon that contains at least one carbon–carbon double bond.
^{[13]}The words alkene and olefin are often used interchangeably. **Alkyne**- Is an unsaturated hydrocarbon containing at least one carbon—carbon triple bond.
^{[14]}The simplest acyclic alkynes with only one triple bond and no other functional groups form a homologous series with the general chemical formula C_{n}H_{2n−2}. **Alloy**- is a combination of metals or of a metal and another element. Alloys are defined by a metallic bonding character.
^{[15]} **Alpha particle**- Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be produced in other ways. Alpha particles are named after the first letter in the Greek alphabet, α.
**Alternating current**- Electrical current that regularly reverses direction.
**Alternative hypothesis**- In statistical hypothesis testing,
the alternative hypothesis (or
*maintained hypothesis*or*research hypothesis*) and the null hypothesis are the two rival hypotheses which are compared by a statistical hypothesis test. In the domain of science two rival hypotheses can be compared by explanatory power and predictive power.. **Ammeter**- An instrument that measures current.
**Amino acids**- Are organic compounds containing amine (-NH
_{2}) and carboxyl (-COOH) functional groups, along with a side chain (R group) specific to each amino acid.^{[16]}^{[17]}^{[18]}The key elements of an amino acid are carbon (C), hydrogen (H), oxygen (O), and nitrogen (N), although other elements are found in the side chains of certain amino acids. About 500 naturally occurring amino acids are known (though only 20 appear in the genetic code) and can be classified in many ways.^{[19]} **Amorphous solid**- An amorphous (from the Greek a, without, morphé, shape, form) or non-crystalline solid is a solid that lacks the long-range order that is characteristic of a crystal.
**Ampere**- The SI unit of current flow, one coulomb per second.
**Amphoterism**- In chemistry, an
**amphoteric**compound is a molecule or ion that can react both as an acid as well as a base.^{[20]}Many metals (such as copper, zinc, tin, lead, aluminium, and beryllium) form amphoteric oxides or hydroxides. Amphoterism depends on the oxidation states of the oxide. Al_{2}O_{3}is an example of an amphoteric oxide.. **Amplifier**- A device that replicates a signal with increased power.
**Amplitude**- The
**amplitude**of a periodic variable is a measure of its change over a single period (such as time or spatial period). There are various definitions of amplitude, which are all functions of the magnitude of the difference between the variable's extreme values. In older texts the phase is sometimes called the amplitude.^{[21]} **Anaerobic digestion**- Is a collection of processes by which microorganisms break down biodegradable material in the absence of oxygen.
^{[22]}The process is used for industrial or domestic purposes to manage waste or to produce fuels. Much of the fermentation used industrially to produce food and drink products, as well as home fermentation, uses anaerobic digestion. **Angular acceleration**- Is the rate of change of angular velocity. In three dimensions, it is a pseudovector. In SI units, it is measured in radians per second squared (rad/s
^{2}), and is usually denoted by the Greek letter alpha (α).^{[23]} **Angular momentum**- In physics, angular momentum (rarely,
*moment of momentum*or*rotational momentum*) is the rotational equivalent of linear momentum. It is an important quantity in physics because it is a conserved quantity—the total angular momentum of a system remains constant unless acted on by an external torque. **Angular velocity**- In physics, the angular velocity of a particle is the rate at which it rotates around a chosen center point: that is, the time rate of change of its angular displacement relative to the origin (i.e. in layman's terms: how quickly an object goes around something over a period of time - e.g. how fast the earth orbits the sun). It is measured in angle per unit time, radians per second in SI units, and is usually represented by the symbol omega (
**ω**, sometimes**Ω**). By convention, positive angular velocity indicates counter-clockwise rotation, while negative is clockwise. **Anion**- Is an ion with more electrons than protons, giving it a net negative charge (since electrons are negatively charged and protons are positively charged).
^{[24]} **Annealing (metallurgy)**- A heat treatment process that relieves internal stresses.
**Annihilation**- In particle physics, annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles, such as an electron colliding with a positron to produce two photons.
^{[25]}The total energy and momentum of the initial pair are conserved in the process and distributed among a set of other particles in the final state. Antiparticles have exactly opposite additive quantum numbers from particles, so the sums of all quantum numbers of such an original pair are zero. Hence, any set of particles may be produced whose total quantum numbers are also zero as long as conservation of energy and conservation of momentum are obeyed.^{[26]} **Anode**- The electrode at which current enters a device such as an electrochemical cell or vacuum tube.
**ANSI**- The
**American National Standards Institute**is a private non-profit organization that oversees the development of voluntary consensus standards for products, services, processes, systems, and personnel in the United States.^{[27]}The organization also coordinates U.S. standards with international standards so that American products can be used worldwide. **Anti-gravity****Anti-gravity**(also known as*non-gravitational field*) is a theory of creating a place or object that is free from the force of gravity. It does not refer to the lack of weight under gravity experienced in free fall or orbit, or to balancing the force of gravity with some other force, such as electromagnetism or aerodynamic lift.**Applied engineering**- Is the field concerned with the application of management, design, and technical skills for the design and integration of systems, the execution of new product designs, the improvement of manufacturing processes, and the management and direction of physical and/or technical functions of a firm or organization. Applied-engineering degreed programs typically include instruction in basic engineering principles, project management, industrial processes, production and operations management, systems integration and control, quality control, and statistics.
^{[28]} **Applied mathematics**- Mathematics used for solutions of practical problems, as opposed to pure mathematics.
**Arc length**- Determining the
**length of an irregular arc segment**is also called rectification of a curve. Historically, many methods were used for specific curves. The advent of infinitesimal calculus led to a general formula that provides closed-form solutions in some cases. **Archimedes' principle****Archimedes' principle**states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid.^{[29]}Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse.^{[30]}**Area moment of inertia**- The
**2nd moment of area**, also known as**moment of inertia of plane area**,**area moment of inertia**, or**second area moment**, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area is typically denoted with either an \({\displaystyle I}\) for an axis that lies in the plane or with a \({\displaystyle J}\) for an axis perpendicular to the plane. In both cases, it is calculated with a multiple integral over the object in question. Its dimension is L (length) to the fourth power. Its unit of dimension when working with the International System of Units is meters to the fourth power, m^{4}. **Arithmetic mean**- In mathematics and statistics, the
**arithmetic mean**or simply the mean or**average**when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection.^{[31]} **Arithmetic progression**- In mathematics, an
**arithmetic progression**(AP) or**arithmetic sequence**is a sequence of numbers such that the difference between the consecutive terms is constant. Difference here means the second minus the first. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with*common difference*of 2. **Aromatic hydrocarbon**- An
**aromatic hydrocarbon**or**arene**^{[32]}(or sometimes**aryl hydrocarbon**)^{[33]}is a hydrocarbon with sigma bonds and delocalized pi electrons between carbon atoms forming a circle. In contrast, aliphatic hydrocarbons lack this delocalization. The term "aromatic" was assigned before the physical mechanism determining aromaticity was discovered; the term was coined as such simply because many of the compounds have a sweet or pleasant odour. The configuration of six carbon atoms in aromatic compounds is known as a benzene ring, after the simplest possible such hydrocarbon, benzene. Aromatic hydrocarbons can be*monocyclic*(MAH) or*polycyclic*(PAH). **Arrhenius equation**- The
**Arrhenius equation**is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that Van 't Hoff's equation for the temperature dependence of equilibrium constants suggests such a formula for the rates of both forward and reverse reactions. This equation has a vast and important application in determining rate of chemical reactions and for calculation of energy of activation. Arrhenius provided a physical justification and interpretation for the formula.^{[34]}^{[35]}^{[36]}Currently, it is best seen as an empirical relationship.^{[37]}^{:188}It can be used to model the temperature variation of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally-induced processes/reactions. The Eyring equation, developed in 1935, also expresses the relationship between rate and energy. **Artificial intelligence**- (AI), is intelligence demonstrated by machines, unlike the natural intelligence displayed by humans and animals. Leading AI textbooks define the field as the study of "intelligent agents": any device that perceives its environment and takes actions that maximize its chance of successfully achieving its goals.
^{[40]}Colloquially, the term "artificial intelligence" is often used to describe machines (or computers) that mimic "cognitive" functions that humans associate with the human mind, such as "learning" and "problem solving".^{[41]} **Assembly language**- A computer programming language where most statements correspond to one or a few machine op-codes.
**Atomic orbital**- In atomic theory and quantum mechanics, an
**atomic orbital**is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom.^{[42]}This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. The term*atomic orbital*may also refer to the physical region or space where the electron can be calculated to be present, as defined by the particular mathematical form of the orbital.^{[43]} **Atomic packing factor**- The percentage of the volume filled with atomic mass in a crystal formation.
**Audio frequency**- An
**audio frequency**(abbreviation:**AF**) or**audible frequency**is characterized as a periodic vibration whose frequency is audible to the average human. The SI unit of audio frequency is the hertz (Hz). It is the property of sound that most determines pitch.^{[44]} **Austenitization****Austenitization**means to heat the iron, iron-based metal, or steel to a temperature at which it changes crystal structure from ferrite to austenite.^{[45]}The more open structure of the austenite is then able to absorb carbon from the iron-carbides in carbon steel. An incomplete initial austenitization can leave undissolved carbides in the matrix.^{[46]}For some irons, iron-based metals, and steels, the presence of carbides may occur during the austenitization step. The term commonly used for this is**two-phase austenitization**.^{[47]}**Automation**- Is the technology by which a process or procedure is performed with minimum human assistance.
^{[48]}Automation^{[49]}or automatic control is the use of various control systems for operating equipment such as machinery, processes in factories, boilers and heat treating ovens, switching on telephone networks, steering and stabilization of ships, aircraft and other applications and vehicles with minimal or reduced human intervention. Some processes have been completely automated. **Autonomous vehicle**- A vehicle capable of driving from one point to another without input from a human operator.
**Azimuthal quantum number**- The
**azimuthal quantum number**is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. The azimuthal quantum number is the second of a set of quantum numbers which describe the unique quantum state of an electron (the others being the principal quantum number, following spectroscopic notation, the magnetic quantum number, and the spin quantum number). It is also known as the**orbital angular momentum**quantum number,**orbital quantum number**or**second quantum number**, and is symbolized as**ℓ**.

**Barometer**- A device for measuring pressure.
**Battery**- Electrochemical cells that transform chemical energy into electricity..
**Base**- In chemistry,
**bases**are substances that, in aqueous solution, release hydroxide (OH^{−}) ions, are slippery to the touch, can taste bitter if an alkali,^{[50]}change the color of indicators (e.g., turn red litmus paper blue), react with acids to form salts, promote certain chemical reactions (base catalysis), accept protons from any proton donor, and/or contain completely or partially displaceable OH^{−}ions. **Baud**- Rate at which data is transferred in symbols/second; a symbol may represent one or more bits.
**Beam**- A structural element whose length is significantly greater than its width or height.
**Beer–Lambert law**- The
**Beer–Lambert law**, also known as**Beer's law**, the**Lambert–Beer law**, or the**Beer–Lambert–Bouguer law**relates the attenuation of light to the properties of the material through which the light is travelling. The law is commonly applied to chemical analysis measurements and used in understanding attenuation in physical optics, for photons, neutrons or rarefied gases. In mathematical physics, this law arises as a solution of the BGK equation. **Belt**- A closed loop of flexible material used to transmit mechancial power from one pulley to another.
**Belt friction**- Is a term describing the friction forces between a belt and a surface, such as a belt wrapped around a bollard. When one end of the belt is being pulled only part of this force is transmitted to the other end wrapped about a surface. The friction force increases with the amount of wrap about a surface and makes it so the tension in the belt can be different at both ends of the belt. Belt friction can be modeled by the Belt friction equation.
^{[51]} **Bending**- In applied mechanics, bending (also known as
*flexure*) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two.^{[52]} **Bending moment**- In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.
^{[53]}^{[54]}The most common or simplest structural element subjected to bending moments is the beam. **Benefit–cost analysis****Cost–benefit analysis**(**CBA**), sometimes called**benefit costs analysis**(**BCA**), is a systematic approach to estimating the strengths and weaknesses of alternatives (for example in transactions, activities, functional business requirements); it is used to determine options that provide the best approach to achieve benefits while preserving savings.^{[55]}It may be used to compare potential (or completed) courses of actions; or estimate (or evaluate) the value against costs of a single decision, project, or policy..**Bernoulli differential equation**- In mathematics, an ordinary differential equation of the form:
- \({\displaystyle y'+P(x)y=Q(x)y^{n}\,}\)

**Bernoulli differential equation**where \({\displaystyle n}\) is any real number and \({\displaystyle n\neq 0}\) and \({\displaystyle n\neq 1}\).^{[56]}It is named after Jacob Bernoulli who discussed it in 1695. Bernoulli equations are special because they are nonlinear differential equations with known exact solutions. A famous special case of the Bernoulli equation is the logistic differential equation. **Bernoulli's equation**- An equation for relating several measurements within a fluid flow, such as velocity, pressure, and potential energy.
**Bernoulli's principle**- In fluid dynamics,
**Bernoulli's principle**states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.^{[57]}^{(Ch.3)}^{[58]}^{(§ 3.5)}The principle is named after Daniel Bernoulli who published it in his book*Hydrodynamica*in 1738.^{[59]}Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler who derived**Bernoulli's equation**in its usual form in 1752.^{[60]}^{[61]}The principle is only applicable for isentropic flows: when the effects of irreversible processes (like turbulence) and non-adiabatic processes (e.g. heat radiation) are small and can be neglected. **Beta particle**- also called
**beta ray**or**beta radiation**(symbol**β**), is a high-energy, high-speed electron or positron emitted by the radioactive decay of an atomic nucleus during the process of beta decay. There are two forms of beta decay, β^{−}decay and β^{+}decay, which produce electrons and positrons respectively.^{[62]} **Binomial distribution**- In probability theory and statistics, the
**binomial distribution**with parameters*n*and*p*is the discrete probability distribution of the number of successes in a sequence of*n*independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: a random variable containing a single bit of information: success/yes/true/one (with probability*p*) or failure/no/false/zero (with probability*q*= 1 −*p*). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e.,*n*= 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance. **Biocatalysis****Biocatalysis**refers to the use of living (biological) systems or their parts to speed up (catalyze) chemical reactions. In biocatalytic processes, natural catalysts, such as enzymes, perform chemical transformations on organic compounds. Both enzymes that have been more or less isolated and enzymes still residing inside living cells are employed for this task.^{[63]}^{[64]}^{[65]}The modern usage of biotechnologically produced and possibly modified enzymes for organic synthesis is termed**chemoenzymatic synthesis**; the reactions performed are**chemoenzymatic reactions**.**Biomedical engineering****Biomedical Engineering**(**BME**) or**Medical Engineering**is the application of engineering principles and design concepts to medicine and biology for healthcare purposes (e.g. diagnostic or therapeutic). This field seeks to close the gap between engineering and medicine, combining the design and problem solving skills of engineering with medical biological sciences to advance health care treatment, including diagnosis, monitoring, and therapy.^{[66]}**Biomimetic****Biomimetics**or**biomimicry**is the imitation of the models, systems, and elements of nature for the purpose of solving complex human problems.^{[67]}**Bionics**- The application of biological methods to engineering systems.
**Biophysics**- Is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena.
^{[68]}^{[69]}^{[70]}Biophysics covers all scales of biological organization, from molecular to organismic and populations. Biophysical research shares significant overlap with biochemistry, molecular biology, physical chemistry, physiology, nanotechnology, bioengineering, computational biology, biomechanics and systems biology. **Biot number**- The
**Biot number**(**Bi**) is a dimensionless quantity used in heat transfer calculations. It is named after the eighteenth century French physicist Jean-Baptiste Biot (1774–1862), and gives a simple index of the ratio of the heat transfer resistances*inside of*and*at the surface of*a body. This ratio determines whether or not the temperatures inside a body will vary significantly in space, while the body heats or cools over time, from a thermal gradient applied to its surface. **Block and tackle**- A system of pulleys and a rope threaded between them, used to lift or pull heavy loads.
**Body force**- Is a force that acts throughout the volume of a body. Forces due to gravity, electric fields and magnetic fields are examples of body forces. Body forces contrast with contact forces or surface forces which are exerted to the surface of an object..
**Boiler**- Is a closed vessel in which fluid (generally water) is heated. The fluid does not necessarily boil. The heated or vaporized fluid exits the boiler for use in various processes or heating applications,
^{[71]}^{[72]}including water heating, central heating, boiler-based power generation, cooking, and sanitation. **Boiling point**- The state at which a substance becomes gaseous.
**Boiling-point elevation****Boiling-point elevation**describes the phenomenon that the boiling point of a liquid (a solvent) will be higher when another compound is added, meaning that a solution has a higher boiling point than a pure solvent. This happens whenever a non-volatile solute, such as a salt, is added to a pure solvent, such as water. The boiling point can be measured accurately using an ebullioscope.**Boltzmann constant**- The
**Boltzmann constant**(*k*_{B}or k) is a physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas^{[73]}and occurs in Planck's law of black-body radiation and in Boltzmann's entropy formula. It was introduced by Max Planck, but named after Ludwig Boltzmann.It is the gas constant R divided by the Avogadro constant*N*_{A}:- \({\displaystyle k={\frac {R}{N_{\text{A}}}}.}\).

- \({\displaystyle \mathbf {R} =n_{1}\mathbf {a} _{1}+n_{2}\mathbf {a} _{2}+n_{3}\mathbf {a} _{3}}\)

**Calculus**- The mathematics of change.
**Capacitance**- The ability of a body to store electrical charge.
**Capacitive reactance**- The impedance of a capacitor in an alternating current circuit, the opposition to current flow.
**Capacitor**- An electrical component that stores energy in an electric field.
**Capillary action****Capillary action**(sometimes**capillarity**,**capillary motion**,**capillary effect**, or**wicking**) is the ability of a liquid to flow in narrow spaces without the assistance of, or even in opposition to, external forces like gravity. The effect can be seen in the drawing up of liquids between the hairs of a paint-brush, in a thin tube, in porous materials such as paper and plaster, in some non-porous materials such as sand and liquefied carbon fiber, or in a cell. It occurs because of intermolecular forces between the liquid and surrounding solid surfaces. If the diameter of the tube is sufficiently small, then the combination of surface tension (which is caused by cohesion within the liquid) and adhesive forces between the liquid and container wall act to propel the liquid.^{[94]}**Carbonate**- Any mineral with bound carbon dioxide.
**Carnot cycle**- A hypothetical thermodynamic cycle for a heat engine; no thermodynamic cycle can be more efficient than a Carnot cycle operating between the same two temperature limits.
**Cartesian coordinates**- Coordinates within a rectangular Cartesian plane.
**Castigliano's method**- Named for Carlo Alberto Castigliano, is a method for determining the displacements of a linear-elastic system based on the partial derivatives of the energy. He is known for his two theorems. The basic concept may be easy to understand by recalling that a change in energy is equal to the causing force times the resulting displacement. Therefore, the causing force is equal to the change in energy divided by the resulting displacement. Alternatively, the resulting displacement is equal to the change in energy divided by the causing force. Partial derivatives are needed to relate causing forces and resulting displacements to the change in energy.
**Casting**- Forming of an object by pouring molten metal (or other substances) into a mold.
**Cathode**- The terminal of a device by which current exits.
**Cathode ray**- The stream of electrons emitted from a heated negative electrode and attracted to a positive electrode.
**Cell membrane**- The
**cell membrane**(also known as the**plasma membrane**or**cytoplasmic membrane,**and historically referred to as the**plasmalemma**) is a biological membrane that separates the interior of all cells from the outside environment (the extracellular space) which protects the cell from its environment^{[95]}^{[96]}consisting of a lipid bilayer with embedded proteins. **Cell nucleus**- In cell biology, the
**nucleus**(pl.; from Latin**nuclei***nucleus*or*nuculeus*, meaning*kernel*or*seed*) is a membrane-enclosed organelle found in eukaryotic cells. Eukaryotes usually have a single nucleus, but a few cell types, such as mammalian red blood cells, have no nuclei, and a few others including osteoclasts have many. **Cell theory**- In biology,
**cell theory**is the historic scientific theory, now universally accepted, that living organisms are made up of cells, that they are the basic structural/organizational unit of all organisms, and that all cells come from pre-existing cells. Cells are the basic unit of structure in all organisms and also the basic unit of reproduction. **Center of gravity**- The center of mass of an object, its balance point.
**Center of mass**- The weighted center of an object; a force applied through the center of mass will not cause rotation of the object.
**Center of pressure**- Is the point where the total sum of a pressure field acts on a body, causing a force to act through that point. The total force vector acting at the center of pressure is the value of the integrated vectorial pressure field. The resultant force and center of pressure location produce equivalent force and moment on the body as the original pressure field.
**Central force motion**- .
**Central limit theorem**- In probability theory, the
**central limit theorem**(**CLT**) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "*bell curve*") even if the original variables themselves are not normally distributed. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. **Central processing unit**- A
**central processing unit**(**CPU**) is the electronic circuitry within a computer that carries out the instructions of a computer program by performing the basic arithmetic, logic, controlling and input/output (I/O) operations specified by the instructions. The computer industry has used the term "central processing unit" at least since the early 1960s.^{[97]}Traditionally, the term "CPU" refers to a**processor**, more specifically to its processing unit and control unit (CU), distinguishing these core elements of a computer from external components such as main memory and I/O circuitry.^{[98]} **Centripetal acceleration**- .
**Centripetal force**- A force acting against rotational acceleration.
**Centroid**- The average point of volume for an object.
**Centrosome**- In cell biology, the
**centrosome**is an organelle that serves as the main microtubule organizing center (MTOC) of the animal cell as well as a regulator of cell-cycle progression. The centrosome is thought to have evolved only in the metazoan lineage of eukaryotic cells.^{[99]}Fungi and plants lack centrosomes and therefore use structures other than MTOCs to organize their microtubules.^{[100]}^{[101]} **Chain reaction**- Is a sequence of reactions where a reactive product or by-product causes additional reactions to take place. In a chain reaction, positive feedback leads to a self-amplifying chain of events.
**Change of base rule**- .
**Charles's law****Charles's law**(also known as the**law of volumes**) is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charles's law is: When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be in direct proportion.^{[102]}**Chemical bond**- Is a lasting attraction between atoms, ions or molecules that enables the formation of chemical compounds. The bond may result from the electrostatic force of attraction between oppositely charged ions as in ionic bonds or through the sharing of electrons as in covalent bonds. The strength of chemical bonds varies considerably; there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force and hydrogen bonding.
**Chemical compound**- Is a chemical substance composed of many identical molecules (or molecular entities) composed of atoms from more than one element held together by chemical bonds. A chemical element bonded to an identical chemical element is not a chemical compound since only one element, not two different elements, is involved.
**Chemical equilibrium**- In a chemical reaction,
**chemical equilibrium**is the state in which both reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system.^{[103]}Usually, this state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but equal. Thus, there are no net changes in the concentrations of the reactant(s) and product(s). Such a state is known as dynamic equilibrium.^{[104]}^{[105]} **Chemical kinetics****Chemical kinetics**, also known as**reaction kinetics**, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that can describe the characteristics of a chemical reaction.**Chemical reaction**- A
**chemical reaction**is a process that leads to the chemical transformation of one set of chemical substances to another.^{[106]}Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur. **Chemistry**- Is the scientific discipline involved with elements and compounds composed of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a reaction with other substances.
^{[107]}^{[108]}^{[109]}^{[110]} **Chloride**- Any chemical compound containing the element chlorine.
**Chromate****Chromate**salts contain the chromate anion, CrO^{2−}_{4}.**Dichromate**salts contain the dichromate anion, Cr^{}_{2}O^{2−}_{7}. They are oxoanions of chromium in the 6+ oxidation state . They are moderately strong oxidizing agents. In an aqueous solution, chromate and dichromate ions can be interconvertible.**Circular motion**- In physics,
**circular motion**is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body. **Civil engineering**- The profession that deals with the design and construction of structures, or other fixed works.
**Clausius–Clapeyron relation**- The
**Clausius–Clapeyron relation**, named after Rudolf Clausius^{[111]}and Benoît Paul Émile Clapeyron,^{[112]}is a way of characterizing a discontinuous phase transition between two phases of matter of a single constituent. On a pressure–temperature (P–T) diagram, the line separating the two phases is known as the coexistence curve. The Clausius–Clapeyron relation gives the slope of the tangents to this curve. Mathematically,- \({\displaystyle {\frac {\mathrm {d} P}{\mathrm {d} T}}={\frac {L}{T\,\Delta v}}={\frac {\Delta s}{\Delta v}},}\)

**Clausius inequality**- .
**Clausius theorem**- The
**Clausius theorem**(1855) states that a system exchanging heat with external reservoirs and undergoing a cyclic process, is one that ultimately returns a system to its original state,- \({\displaystyle \oint {\frac {\delta Q}{T_{surr}}}\leq 0,}\)

^{[113]}The reversible case is used to introduce the entropy state function. This is because in a cyclic process the variation of a state function is zero. In words, the Clausius statement states that it is impossible to construct a device whose sole effect is the transfer of heat from a cool reservoir to a hot reservoir.^{[114]}Equivalently, heat spontaneously flows from a hot body to a cooler one, not the other way around.^{[115]}The generalized "inequality of Clausius"^{[116]}- \({\displaystyle dS>{\frac {\delta Q}{T_{surr}}}}\)

*S*applies not only to cyclic processes, but to any process that occurs in a closed system. **Coefficient of performance**- The
**coefficient of performance**or**COP**(sometimes**CP**or**CoP**) of a heat pump, refrigerator or air conditioning system is a ratio of useful heating or cooling provided to work required.^{[117]}^{[118]}Higher COPs equate to lower operating costs. The COP usually exceeds 1, especially in heat pumps, because, instead of just converting work to heat (which, if 100% efficient, would be a COP_hp of 1), it pumps additional heat from a heat source to where the heat is required. For complete systems, COP calculations should include energy consumption of all power consuming auxiliaries. COP is highly dependent on operating conditions, especially absolute temperature and relative temperature between sink and system, and is often graphed or averaged against expected conditions.^{[119]} **Coefficient of variation**- In probability theory and statistics, the
**coefficient of variation**(**CV**), also known as**relative standard deviation**(**RSD**), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage, and is defined as the ratio of the standard deviation \({\displaystyle \ \sigma }\) to the mean \({\displaystyle \ \mu }\) (or its absolute value, \({\displaystyle |\mu |}\)). **Coherence**- In physics, two wave sources are perfectly coherent if they have a constant phase difference and the same frequency, and the same waveform. Coherence is an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference. It contains several distinct concepts, which are limiting cases that never quite occur in reality but allow an understanding of the physics of waves, and has become a very important concept in quantum physics. More generally,
**coherence**describes all properties of the correlation between physical quantities of a single wave, or between several waves or wave packets. **Cohesion**- Or
**cohesive attraction**or**cohesive force**is the action or property of like molecules sticking together, being mutually attractive. It is an intrinsic property of a substance that is caused by the shape and structure of its molecules, which makes the distribution of orbiting electrons irregular when molecules get close to one another, creating electrical attraction that can maintain a microscopic structure such as a water drop. In other words, cohesion allows for surface tension, creating a "solid-like" state upon which light-weight or low-density materials can be placed. **Cold forming**- Or
**cold working**, any metal-working procedure (such as hammering, rolling, shearing, bending, milling, etc.) carried out below the metal's recrystallization temperature. **Combustion**- Or
**burning**,^{[120]}is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. **Compensation**- Is planning for side effects or other unintended issues in a design. In a more simpler term, it's a "counter-procedure" plan on expected side effect performed to produce more efficient and useful results. The design of an invention can itself also be to compensate for some other existing issue or exception.
**Compiler**- A computer program that translates a high-level language into machine language.
**Compressive strength****Compressive strength**or**compression strength**is the capacity of a material or structure to withstand loads tending to reduce size, as opposed to tensile strength, which withstands loads tending to elongate. In other words, compressive strength resists compression (being pushed together), whereas tensile strength resists tension (being pulled apart). In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently.**Computational fluid dynamics**- The numerical solution of flow equations in practical problems such as aircraft design or hydraulic structures.
**Computer**- A
**computer**is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming. Modern computers have the ability to follow generalized sets of operations, called*programs.*These programs enable computers to perform an extremely wide range of tasks. **Computer-aided design****Computer-aided design**(**CAD**) is the use of computer systems (or workstations) to aid in the creation, modification, analysis, or optimization of a design.^{[121]}CAD software is used to increase the productivity of the designer, improve the quality of design, improve communications through documentation, and to create a database for manufacturing.^{[122]}CAD output is often in the form of electronic files for print, machining, or other manufacturing operations. The term**CADD**(for*Computer Aided Design and Drafting*) is also used.^{[123]}**Computer-aided engineering****Computer-aided engineering**(**CAE**) is the broad usage of computer software to aid in engineering analysis tasks. It includes finite element analysis (FEA), computational fluid dynamics (CFD), multibody dynamics (MBD), durability and optimization.**Computer-aided manufacturing****Computer-aided manufacturing**(**CAM**) is the use of software to control machine tools and related ones in the manufacturing of workpieces.^{[124]}^{[125]}^{[126]}^{[127]}^{[128]}This is not the only definition for CAM, but it is the most common;^{[124]}CAM may also refer to the use of a computer to assist in all operations of a manufacturing plant, including planning, management, transportation and storage.^{[129]}^{[130]}**Computer engineering****Computer engineering**is a discipline that integrates several fields of computer science and electronics engineering required to develop computer hardware and software.^{[131]}**Computer science**- Is the theory, experimentation, and engineering that form the basis for the design and use of computers. It involves the study of algorithms that process, store, and communicate digital information. A computer scientist specializes in the theory of computation and the design of computational systems.
^{[132]} **Concave lens**- Lenses are classified by the curvature of the two optical surfaces. A lens is
*biconvex*(or*double convex*, or just*convex*) if both surfaces are convex. If both surfaces have the same radius of curvature, the lens is*equiconvex*. A lens with two concave surfaces is*biconcave*(or just*concave*). If one of the surfaces is flat, the lens is*plano-convex*or*plano-concave*depending on the curvature of the other surface. A lens with one convex and one concave side is*convex-concave*or*meniscus*. **Condensed matter physics**- Is the field of physics that deals with the macroscopic and microscopic physical properties of matter. In particular it is concerned with the "condensed" phases that appear whenever the number of constituents in a system is extremely large and the interactions between the constituents are strong.
**Confidence interval**- In statistics, a
**confidence interval**or**compatibility interval**(**CI**) is a type of interval estimate, computed from the statistics of the observed data, that might contain the true value of an unknown population parameter. The interval has an associated**confidence level**that, loosely speaking, quantifies the level of confidence that the parameter lies in the interval. More strictly speaking, the**confidence level**represents the frequency (i.e. the proportion) of possible confidence intervals that contain the true value of the unknown population parameter. In other words, if confidence intervals are constructed using a given confidence level from an infinite number of independent sample statistics, the proportion of those intervals that contain the true value of the parameter will be equal to the confidence level.^{[133]}^{[134]}^{[135]} **Conjugate acid**- A
**conjugate acid**, within the Brønsted–Lowry acid–base theory, is a species formed by the reception of a proton (H^{+}) by a base—in other words, it is a base with a hydrogen ion added to it. On the other hand, a**conjugate base**is what is left over after an acid has donated a proton during a chemical reaction. Hence, a conjugate base is a species formed by the removal of a proton from an acid.^{[136]}Because some acids are capable of releasing multiple protons, the conjugate base of an acid may itself be acidic. **Conjugate base**- A
**conjugate acid**, within the Brønsted–Lowry acid–base theory, is a species formed by the reception of a proton (H^{+}) by a base—in other words, it is a base with a hydrogen ion added to it. On the other hand, a**conjugate base**is what is left over after an acid has donated a proton during a chemical reaction. Hence, a conjugate base is a species formed by the removal of a proton from an acid.^{[136]}Because some acids are capable of releasing multiple protons, the conjugate base of an acid may itself be acidic.. **Conservation of energy**- In physics and chemistry, the
**law of conservation of energy**states that the total energy of an isolated system remains constant; it is said to be*conserved*over time.^{[137]}This law means that energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. **Conservation of mass**- The
**law of conservation of mass**or**principle of mass conservation**states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as system's mass cannot change, so quantity cannot be added nor removed. Hence, the quantity of mass is conserved over time. **Continuity equation**- A
**continuity equation**in physics is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described using continuity equations. **Continuum mechanics**- Is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century.
**Control engineering****Control engineering**or**control systems engineering**is an engineering discipline that applies automatic control theory to design systems with desired behaviors in control environments.^{[138]}The discipline of controls overlaps and is usually taught along with electrical engineering at many institutions around the world.^{[138]}.**Convex lens**- Lenses are classified by the curvature of the two optical surfaces. A lens is
*biconvex*(or*double convex*, or just*convex*) if both surfaces are convex. If both surfaces have the same radius of curvature, the lens is*equiconvex*. A lens with two concave surfaces is*biconcave*(or just*concave*). If one of the surfaces is flat, the lens is*plano-convex*or*plano-concave*depending on the curvature of the other surface. A lens with one convex and one concave side is*convex-concave*or*meniscus*. **Corrosion**- Is a natural process, which converts a refined metal to a more chemically-stable form, such as its oxide, hydroxide, or sulfide. It is the gradual destruction of materials (usually metals) by chemical and/or electrochemical reaction with their environment. Corrosion engineering is the field dedicated to controlling and stopping corrosion.
**Cosmic rays****Cosmic rays**are high-energy radiation, mainly originating outside the Solar System.^{[139]}**Coulomb**- The
**coulomb**(symbol: C) is the International System of Units (SI) unit of electric charge. It is the charge (symbol:*Q*or*q*) transported by a constant current of one ampere in one second:- \({\displaystyle 1~{\text{C}}=1~{\text{A}}\cdot 1~{\text{s}}}\)

- \({\displaystyle 1~{\text{C}}=1~{\text{F}}\cdot 1~{\text{V}}}\)

^{18}(1.036×10^{−5}mol) protons, and −1 C is equivalent to the charge of approximately 6.242×10^{18}electrons.A new definition, in terms of the elementary charge, will take effect on 20 May 2019.^{[140]}The new definition, defines the elementary charge (the charge of the proton) as exactly 1.602176634×10^{−19}coulombs. This would implicitly define the coulomb as 1⁄0.1602176634×10^{18}elementary charges. **Coulomb's law****Coulomb's law**, or**Coulomb's inverse-square law**, is a law of physics for quantifying Coulomb's force, or electrostatic force. Electrostatic force is the amount of force with which stationary, electrically charged particles either repel, or attract each other. This force and the law for quantifying it, represent one of the most basic forms of force used in the physical sciences, and were an essential basis to the study and development of the theory and field of classical electromagnetism. The law was first published in 1785 by French physicist Charles-Augustin de Coulomb.^{[141]}In its scalar form, the law is:- \({\displaystyle F=k_{e}{\frac {q_{1}q_{2}}{r^{2}}}}\),

*k*_{e}is Coulomb's constant (*k*_{e}≈ 9×10^{9}N m^{2}C^{−2}),*q*_{1}and*q*_{2}are the signed magnitudes of the charges, and the scalar*r*is the distance between the charges. The force of the interaction between the charges is attractive if the charges have opposite signs (i.e.,*F*is negative) and repulsive if like-signed (i.e.,*F*is positive).Being an inverse-square law, the law is analogous to Isaac Newton's inverse-square law of universal gravitation. Coulomb's law can be used to derive Gauss's law, and vice versa.**Covalent bond**- A
**covalent bond**, also called a**molecular bond**, is a chemical bond that involves the sharing of electron pairs between atoms. **Crookes tube**- A type of vacuum tube that demonstrates cathode rays.
**Cryogenics**- The science of low temperatures.
**Crystallization****Crystallization**is the (natural or artificial) process by which a solid forms, where the atoms or molecules are highly organized into a structure known as a crystal. Some of the ways by which crystals form are precipitating from a solution, freezing, or more rarely deposition directly from a gas. Attributes of the resulting crystal depend largely on factors such as temperature, air pressure, and in the case of liquid crystals, time of fluid evaporation.**Crystallography**- The study of crystals.
**Curvilinear motion**- Describes the motion of a moving particle that conforms to a known or fixed curve. The study of such motion involves the use of two co-ordinate systems, the first being planar motion and the latter being cylindrical motion.
**Cyclotron**- A
**cyclotron**is a type of particle accelerator invented by Ernest O. Lawrence in 1929-1930 at the University of California, Berkeley,^{[142]}^{[143]}and patented in 1932.^{[144]}^{[145]}A cyclotron accelerates charged particles outwards from the center along a spiral path.^{[146]}^{[147]}The particles are held to a spiral trajectory by a static magnetic field and accelerated by a rapidly varying (radio frequency) electric field. Lawrence was awarded the 1939 Nobel prize in physics for this invention.^{[147]}^{[148]}

**Dalton's law**- In chemistry and physics,
**Dalton's law**(also called**Dalton's law of partial pressures**) states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases.^{[149]} **Damped vibration**- Any vibration with a force acting against it to lessen the vibration over time.
**Darcy–Weisbach equation**- An equation used in fluid mechanics to find the pressure change cause by friction within a pipe or conduit.
**DC motor**- An electrical motor driven by direct current.
**Decibel**- A logarithmic unit of ratios.
**Definite integral**- The integral of a function between an upper and lower limit.
^{[150]} **Deflection**- Is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance.
**Deformation (engineering)**- In materials science,
**deformation**refers to any changes in the shape or size of an object due to- an applied force (the deformation energy in this case is transferred through work) or
- a change in temperature (the deformation energy in this case is transferred through heat).

^{[151]}^{[152]} **Deformation (mechanics)****Deformation**in continuum mechanics is the transformation of a body from a*reference*configuration to a*current*configuration.^{[153]}A configuration is a set containing the positions of all particles of the body.A deformation may be caused by external loads,^{[154]}body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc.**Degrees of freedom**- The number of parameters required to define the motion of a dynamical system.
**Delta robot**- A tripod linkage, used to construct fast-acting manipulators with a wide range of movement.
**Delta-wye transformer**- A type of transformer used in three-phase power systems.
**De Moivre–Laplace theorem**- In probability theory, the
**de Moivre–Laplace theorem**, which is a special case of the central limit theorem, states that the normal distribution may be used as an approximation to the binomial distribution under certain conditions. In particular, the theorem shows that the probability mass function of the random number of "successes" observed in a series of \({\displaystyle n}\) independent Bernoulli trials, each having probability \({\displaystyle p}\) of success (a binomial distribution with \({\displaystyle n}\) trials), converges to the probability density function of the normal distribution with mean \({\displaystyle np}\) and standard deviation\({\displaystyle {\sqrt {np(1-p)}}}\), as \({\displaystyle n}\) grows large, assuming \({\displaystyle p}\) is not \({\displaystyle 0}\) or \({\displaystyle 1}\). **Density**- The
**density**, or more precisely, the**volumetric mass density**, of a substance is its mass per unit volume. The symbol most often used for density is*ρ*(the lower case Greek letter rho), although the Latin letter*D*can also be used. Mathematically, density is defined as mass divided by volume:^{[155]}- \({\displaystyle \rho ={\frac {m}{V}}}\)

*ρ*is the density,*m*is the mass, and*V*is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume,^{[156]}although this is scientifically inaccurate – this quantity is more specifically called specific weight. **Derivative**- The
**derivative**of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. **Design engineering**- .
**Dew point**- The pressure and temperature at which air is holding the maximum possible humidity.
**Diamagnetism****Diamagnetic**materials are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted by a magnetic field.**Diamagnetism**is a quantum mechanical effect that occurs in all materials; when it is the only contribution to the magnetism, the material is called diamagnetic. In paramagnetic and ferromagnetic substances the weak diamagnetic force is overcome by the attractive force of magnetic dipoles in the material. The magnetic permeability of diamagnetic materials is less than μ_{0}, the permeability of vacuum. In most materials diamagnetism is a weak effect which can only be detected by sensitive laboratory instruments, but a superconductor acts as a strong diamagnet because it repels a magnetic field entirely from its interior.**Dielectric**- An insulator, a material that does not permit free flow of electricity.
**Differential pressure**- .
**Differential pulley**- A
**differential pulley**, also called**Weston differential pulley**, or colloquially**chain fall**, is used to manually lift very heavy objects like car engines. It is operated by pulling upon the slack section of a continuous chain that wraps around pulleys. The relative size of two connected pulleys determines the maximum weight that can be lifted by hand. The load will remain in place (and not lower under the force of gravity) until the chain is pulled.^{[157]} **Differential signaling**- Is a method for electrically transmitting information using two complementary signals.
**Diffusion**- Is the net movement of molecules or atoms from a region of higher concentration (or high chemical potential) to a region of lower concentration (or low chemical potential).
**Dimensional analysis**- is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. The conversion of units from one dimensional unit to another is often somewhat complex. Dimensional analysis, or more specifically the
**factor-label method**, also known as the**unit-factor method**, is a widely used technique for such conversions using the rules of algebra.^{[158]}^{[159]}^{[160]} **Direct integration of a beam****Direct integration**is a structural analysis method for measuring internal shear, internal moment, rotation, and deflection of a beam.For a beam with an applied weight \({\displaystyle w(x)}\), taking downward to be positive, the internal shear force is given by taking the negative integral of the weight:- \({\displaystyle V(x)=-\int w(x)\,dx}\)

- \({\displaystyle M(x)=\int V(x)\,dx}\) = \({\displaystyle -\int [\int w(x)\ \,dx]dx}\)

- \({\displaystyle \theta (x)={\frac {1}{EI}}\int M(x)\,dx}\)

- \({\displaystyle \nu (x)=\int \theta (x)dx}\).

**Economics**- The scientific study of the production, distribution and consumption of goods.
**Effusion**- In physics and chemistry, effusion is the process in which a gas escapes from a container through a hole of diameter considerably smaller than the mean free path of the molecules.
^{[169]} **Elastic modulus**- The amount a material will deform per unit force.
**Elasticity**- In physics, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate forces are applied to them. If the material is elastic, the object will return to its initial shape and size when these forces are removed.
**Electric charge**- is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges;
*positive*and*negative*(commonly carried by protons and electrons respectively). Like charges repel and unlike attract. An object with an absence of net charge is referred to as*neutral*. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum effects. **Electric circuit**- Is an electrical network consisting of a closed loop, giving a return path for the current.
**Electric current**- Is a flow of electric charge.
^{[170]}^{:2}In electric circuits this charge is often carried by moving electrons in a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in an ionised gas (plasma).^{[171]}The SI unit for measuring an electric current is the ampere, which is the flow of electric charge across a surface at the rate of one coulomb per second. Electric current is measured using a device called an ammeter.^{[172]} **Electric displacement field**- In physics, the
**electric displacement field**, denoted by**D**, is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "**D**" stands for "displacement", as in the related concept of displacement current in dielectrics. In free space, the electric displacement field is equivalent to flux density, a concept that lends understanding to Gauss's law. In the International System of Units (SI), it is expressed in units of coulomb per meter squared (C⋅m^{−2}). **Electric generator**- In electricity generation, a
**generator**,also called**electric generator**,**electrical generator**, and**electromagnetic generator**. is a device that converts motive power (mechanical energy) into electrical power for use in an external circuit. Sources of mechanical energy include steam turbines, gas turbines, water turbines, internal combustion engines and even hand cranks. **Electric field**- Surrounds an electric charge, and exerts force on other charges in the field, attracting or repelling them.
^{[173]}^{[174]}Electric field is sometimes abbreviated as**E-field**. **Electric field gradient**- In atomic, molecular, and solid-state physics, the
**electric field gradient**(**EFG**) measures the rate of change of the electric field at an atomic nucleus generated by the electronic charge distribution and the other nuclei. **Electric motor**- Is an electrical machine that converts electrical energy into mechanical energy. Most electric motors operate through the interaction between the motor's magnetic field and winding currents to generate force in the form of rotation. Electric motors can be powered by direct current (DC) sources, such as from batteries, motor vehicles or rectifiers, or by alternating current (AC) sources, such as a power grid, inverters or electrical generators. An electric generator is mechanically identical to an electric motor, but operates in the reverse direction, accepting mechanical energy (such as from flowing water) and converting this mechanical energy into electrical energy.
**Electric potential**- (Also called the
*electric field potential*, potential drop or the**electrostatic potential**) is the amount of work needed to move a unit of positive charge from a reference point to a specific point inside the field without producing an acceleration. Typically, the reference point is the Earth or a point at infinity, although any point beyond the influence of the electric field charge can be used. **Electrical potential energy**- Electric potential energy, or electrostatic potential energy, is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An
*object*may have electric potential energy by virtue of two key elements: its own electric charge and its relative position to other electrically charged*objects*. The term "electric potential energy" is used to describe the potential energy in systems with time-variant electric fields, while the term "electrostatic potential energy" is used to describe the potential energy in systems with time-invariant electric fields. **Electric power**- Is the rate, per unit time, at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second..
**Electrical engineering**- Is a technical discipline concerned with the study, design and application of equipment, devices and systems which use electricity, electronics, and electromagnetism. It emerged as an identified activity in the latter half of the 19th century after commercialization of the electric telegraph, the telephone, and electrical power generation, distribution and use. .
**Electrical conductance**- The electrical resistance of an object is a measure of its opposition to the flow of electric current. The inverse quantity is electrical conductance, and is the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with the notion of mechanical friction. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S).
**Electrical conductor**- Is an object or type of material that allows the flow of charge (electrical current) in one or more directions. Materials made of metal are common electrical conductors. Electrical current is generated by the flow of negatively charged electrons, positively charged holes, and positive or negative ions in some cases.
**Electrical impedance**- Is the measure of the opposition that a circuit presents to a current when a voltage is applied. The term
*complex impedance*may be used interchangeably. **Electrical insulator**- Is a material whose internal electric charges do not flow freely; very little electric current will flow through it under the influence of an electric field. This contrasts with other materials, semiconductors and conductors, which conduct electric current more easily. The property that distinguishes an insulator is its resistivity; insulators have higher resistivity than semiconductors or conductors.
**Electrical network**- Is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, current sources, resistances, inductances, capacitances). An electrical circuit is a network consisting of a closed loop, giving a return path for the current. Linear electrical networks, a special type consisting only of sources (voltage or current), linear lumped elements (resistors, capacitors, inductors), and linear distributed elements (transmission lines), have the property that signals are linearly superimposable. They are thus more easily analyzed, using powerful frequency domain methods such as Laplace transforms, to determine DC response, AC response, and transient response.
**Electrical resistance**- The electrical resistance of an object is a measure of its opposition to the flow of electric current. The inverse quantity is electrical conductance, and is the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with the notion of mechanical friction. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S).
**Electricity**- Is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwell's equations. Various common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges and many others.
**Electrodynamics**- In physics, the phenomena associated with moving electric charges, and their interaction with electric and magnetic fields; the study of these phenomena.
^{[175]} **Electromagnet**- Is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire wound into a coil. A current through the wire creates a magnetic field which is concentrated in the hole, denoting the centre of the coil. The magnetic field disappears when the current is turned off. The wire turns are often wound around a magnetic core made from a ferromagnetic or ferrimagnetic material such as iron; the magnetic core concentrates the magnetic flux and makes a more powerful magnet.
**Electromagnetic field**- An electromagnetic field (also
*EM field*) is a classical (i.e. non-quantum) field produced by accelerating electric charges.^{[176]}It is the field described by classical electrodynamics and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics. The electromagnetic field propagates at the speed of light (in fact, this field can be identified*as*light) and interacts with charges and currents. Its quantum counterpart is one of the four fundamental forces of nature (the others are gravitation, weak interaction and strong interaction.) **Electromagnetic radiation**- In physics, electromagnetic radiation (
*EM radiation*or*EMR*) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy.^{[177]}It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays.^{[178]} **Electromechanics**- Electromechanics
^{[179]}^{[180]}^{[181]}^{[182]}combines processes and procedures drawn from electrical engineering and mechanical engineering. Electromechanics focuses on the interaction of electrical and mechanical systems as a whole and how the two systems interact with each other. This process is especially prominent in systems such as those of DC or AC rotating electrical machines which can be designed and operated to generate power from a mechanical process (generator) or used to power a mechanical effect (motor). Electrical engineering in this context also encompasses electronics engineering. **Electron**- Is a subatomic particle, symbol
^{}_{}e^{−}_{}or^{}_{}β^{−}_{}, whose electric charge is negative one elementary charge.^{[183]}Electrons belong to the first generation of the lepton particle family,^{[184]}and are generally thought to be elementary particles because they have no known components or substructure.^{[185]}The electron has a mass that is approximately 1/1836 that of the proton.^{[186]}Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant,*ħ*. Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle.^{[184]}Like all elementary particles, electrons exhibit properties of both particles and waves: they can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy. **Electronvolt**- In physics, an electronvolt (symbol eV, also written
*electron-volt*and*electron volt*) is the amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. When used as a unit of energy, the numerical value of 1 eV in joules (symbol J) is equivalent to the numerical value of the charge of an electron in coulombs (symbol C). Under the 2019 redefinition of the SI base units, this sets 1 eV equal to the exact value 1.602176634×10^{−19}J.^{[187]} **Electron pair**- In chemistry, an electron pair, or
*Lewis pair*, consists of two electrons that occupy the same molecular orbital but have opposite spins. Gilbert N. Lewis introduced the concepts of both the electron pair and the covalent bond in a landmark paper he published in 1916.^{[188]} **Electronegativity**- Symbolized as
*χ*, is the measurement of the tendency of an atom to attract a shared pair of electrons (or electron density).^{[189]}An atom's electronegativity is affected by both its atomic number and the distance at which its valence electrons reside from the charged nucleus. The higher the associated electronegativity, the more an atom or a substituent group attracts electrons. **Electronics**- Comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter.
^{[190]}It uses active devices to control electron flow by amplification and rectification, which distinguishes it from classical electrical engineering which uses passive effects such as resistance, capacitance and inductance to control current flow. **Elemental analysis**- Is a process where a sample of some material (e.g., soil, waste or drinking water, bodily fluids, minerals, chemical compounds) is analyzed for its elemental and sometimes isotopic composition.
^{[citation needed]}Elemental analysis can be qualitative (determining what elements are present), and it can be quantitative (determining how much of each are present). Elemental analysis falls within the ambit of analytical chemistry, the set of instruments involved in deciphering the chemical nature of our world. **Endothermic process**- Is any process with an increase in the enthalpy
*H*(or internal energy*U*) of the system.^{[191]}In such a process, a closed system usually absorbs thermal energy from its surroundings, which is heat transfer into the system. It may be a chemical process, such as dissolving ammonium nitrate in water, or a physical process, such as the melting of ice cubes. **Energy**- In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.
^{[note 1]}Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton. **Engine**- An engine or
*motor*is a machine designed to convert one form of energy into mechanical energy.^{[192]}^{[193]}Heat engines convert heat into work via various thermodynamic processes. The internal combustion engine is perhaps the most common example of a heat engine, in which heat from the combustion of a fuel causes rapid pressurisation of the gaseous combustion products in the combustion chamber, causing them to expand and drive a piston, which turns a crankshaft. Electric motors convert electrical energy into mechanical motion, pneumatic motors use compressed air, and clockwork motors in wind-up toys use elastic energy. In biological systems, molecular motors, like myosins in muscles, use chemical energy to create forces and ultimately motion. **Engineering**- Is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings.
^{[194]}The discipline of engineering encompasses a broad range of more specialized fields of engineering, each with a more specific emphasis on particular areas of applied mathematics, applied science, and types of application. The term*engineering*is derived from the Latin*ingenium*, meaning "cleverness" and*ingeniare*, meaning "to contrive, devise".^{[195]} **Engineering economics**- Engineering economics, previously known as
*engineering economy*, is a subset of economics concerned with the use and "...application of economic principles"^{[196]}in the analysis of engineering decisions.^{[197]}As a discipline, it is focused on the branch of economics known as microeconomics in that it studies the behavior of individuals and firms in making decisions regarding the allocation of limited resources. Thus, it focuses on the decision making process, its context and environment.^{[196]}It is pragmatic by nature, integrating economic theory with engineering practice.^{[196]}But, it is also a simplified application of microeconomic theory in that it assumes elements such as price determination, competition and demand/supply to be fixed inputs from other sources.^{[196]}As a discipline though, it is closely related to others such as statistics, mathematics and cost accounting.^{[196]}It draws upon the logical framework of economics but adds to that the analytical power of mathematics and statistics.^{[196]} **Engineering ethics**- Is the field of system of moral principles that apply to the practice of engineering. The field examines and sets the obligations by engineers to society, to their clients, and to the profession. As a scholarly discipline, it is closely related to subjects such as the philosophy of science, the philosophy of engineering, and the ethics of technology.
**Environmental engineering**- Is a job type that is a professional engineering discipline and takes from broad scientific topics like chemistry, biology, ecology, geology, hydraulics, hydrology, microbiology, and mathematics to create solutions that will protect and also improve the health of living organisms and improve the quality of the environment.
^{[198]}^{[199]}Environmental engineering is a sub-discipline of civil engineering and chemical engineering. **Engineering physics**- Or
*engineering science*, refers to the study of the combined disciplines of physics, mathematics, chemistry, biology, and engineering, particularly computer, nuclear, electrical, electronic, aerospace, materials or mechanical engineering. By focusing on the scientific method as a rigorous basis, it seeks ways to apply, design, and develop new solutions in engineering.^{[200]}^{[201]}^{[202]}^{[203]} **Enzyme**- Enzymes are proteins that act as biological catalysts (biocatalysts). Catalysts accelerate chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. Almost all metabolic processes in the cell need enzyme catalysis in order to occur at rates fast enough to sustain life.
^{[204]}^{:8.1} **Escape velocity**- The minimum velocity at which an object can escape a gravitation field..
**Estimator**- In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished.
^{[205]}For example, the sample mean is a commonly used estimator of the population mean. There are point and interval estimators. The point estimators yield single-valued results, although this includes the possibility of single vector-valued results and results that can be expressed as a single function. This is in contrast to an interval estimator, where the result would be a range of plausible values (or vectors or functions). **Euler–Bernoulli beam theory**- Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory)
^{[206]}is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case for small deflections of a beam that are subjected to lateral loads only. It is thus a special case of Timoshenko beam theory. It was first enunciated circa 1750,^{[207]}but was not applied on a large scale until the development of the Eiffel Tower and the Ferris wheel in the late 19th century. Following these successful demonstrations, it quickly became a cornerstone of engineering and an enabler of the Second Industrial Revolution. Additional mathematical models have been developed such as plate theory, but the simplicity of beam theory makes it an important tool in the sciences, especially structural and mechanical engineering. **Exothermic process**- In thermodynamics, the term exothermic process (exo- : "outside") describes a process or reaction that releases energy from the system to its surroundings, usually in the form of heat, but also in a form of light (e.g. a spark, flame, or flash), electricity (e.g. a battery), or sound (e.g. explosion heard when burning hydrogen). Its etymology stems from the Greek prefix
*έξω*(exō, which means "outwards") and the Greek word*θερμικός*(thermikόs, which means "thermal").^{[208]}

**Factor of safety**- (
**FoS**), also known as (and used interchangeably with)**safety factor**(**SF**), expresses how much stronger a system is than it needs to be for an intended load. **Falling bodies**- .
**Farad**^{[209]}The farad (symbol: F) is the SI derived unit of electrical capacitance, the ability of a body to store an electrical charge. It is named after the English physicist Michael Faraday..**Faraday constant**- Denoted by the symbol
*F*and sometimes stylized as ℱ, is named after Michael Faraday. In physics and chemistry, this constant represents the magnitude of electric charge per mole of electrons.^{[210]}It has the value- 96485.33212... C mol
^{−1}.^{[211]}

- \({\displaystyle F\,=\,eN_{A}}\)

*e*= 1.602176634×10^{−19}C;^{[212]}*N*_{A}= 6.02214076×10^{23}mol^{−1}.^{[213]}

*F*has a known exact value.*N*_{A}is the Avogadro constant (the ratio of the number of particles,*N*, which is unitless, to the amount of substance,*n*, in units of moles), and*e*is the elementary charge or the magnitude of the charge of an electron. This relation holds because the amount of charge of a mole of electrons is equal to the amount of charge in*one*electron multiplied by the number of electrons in a mole. - 96485.33212... C mol
**Fermat's principle**- In optics, Fermat's principle, or the
*principle of least time*, named after French mathematician Pierre de Fermat, is the principle that the path taken between two points by a ray of light is the path that can be traversed in the least time. This principle is sometimes taken as the definition of a ray of light.^{[214]}However, this version of the principle is not general; a more modern statement of the principle is that rays of light traverse the path of stationary optical length with respect to variations of the path.^{[215]}In other words, a ray of light prefers the path such that there are other paths, arbitrarily nearby on either side, along which the ray would take almost exactly the same time to traverse. **Fick's laws of diffusion**- Describe diffusion and were derived by Adolf Fick in 1855. They can be used to solve for the diffusion coefficient, D. Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation.
**Finite element method**- (FEM), is the most widely used method for solving problems of engineering and mathematical models. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.
The FEM is a particular numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points.
The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain.
^{[216]}The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. The FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function. **FIRST**- For Inspiration and Recognition of Science and Technology – is an organization founded by inventor Dean Kamen in 1989 to develop ways to inspire students in engineering and technology fields.
**Fission**- In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction or a radioactive decay process in which the nucleus of an atom splits into two or more smaller, lighter nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactive decay.
**Flow velocity**- In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity
^{[217]}^{[218]}in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar. It is also called velocity field; when evaluated along a line, it is called a velocity profile (as in, e.g., law of the wall). **Fluid**- In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress, or external force. Fluids are a phase of matter and include liquids, gases and plasmas. They are substances with zero shear modulus, or, in simpler terms, substances which cannot resist any shear force applied to them.
**Fluid dynamics**- In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion).
**Fluid mechanics**- Is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.
^{[219]}It has applications in a wide range of disciplines, including mechanical, civil, chemical and biomedical engineering, geophysics, oceanography, meteorology, astrophysics, and biology. **Fluid statics**- Fluid statics, or
*hydrostatics*, is the branch of fluid mechanics that studies "fluids at rest and the pressure in a fluid or exerted by a fluid on an immersed body".^{[220]} **Flywheel**- Is a mechanical device specifically designed to use the conservation of angular momentum so as to efficiently store rotational energy; a form of kinetic energy proportional to the product of its moment of inertia and the square of its rotational speed. In particular, if we assume the flywheel's moment of inertia to be constant (i.e., a flywheel with fixed mass and second moment of area revolving about some fixed axis) then the stored (rotational) energy is directly associated with the square of its rotational speed.
**Focus**- In geometrical optics, a focus, also called an
*image point*, is the point where light rays originating from a point on the object converge.^{[221]}Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by aberrations of the imaging optics. In the absence of significant aberrations, the smallest possible blur circle is the Airy disc, which is caused by diffraction from the optical system's aperture. Aberrations tend worsen as the aperture diameter increases, while the Airy circle is smallest for large apertures. **Foot-pound**- The foot-pound force (symbol: ft⋅lbf,
^{[222]}ft⋅lb_{f},^{[223]}or ft⋅lb^{[224]}) is a unit of work or energy in the engineering and gravitational systems in United States customary and imperial units of measure. It is the energy transferred upon applying a force of one pound-force (lbf) through a linear displacement of one foot. The corresponding SI unit is the joule. **Fracture toughness**- In materials science, fracture toughness is the critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited. A component's thickness affects the constraint conditions at the tip of a crack with thin components having plane stress conditions and thick components having plane strain conditions. Plane strain conditions give the lowest fracture toughness value which is a material property. The critical value of stress intensity factor in mode I loading measured under plane strain conditions is known as the
*plane strain fracture toughness*, denoted \({\displaystyle K_{\text{Ic}}}\).^{[225]}When a test fails to meet the thickness and other test requirements that are in place to ensure plane strain conditions, the fracture toughness value produced is given the designation \({\displaystyle K_{\text{c}}}\). Fracture toughness is a quantitative way of expressing a material's resistance to crack propagation and standard values for a given material are generally available. **Fraunhofer lines**- In physics and optics, the Fraunhofer lines are a set of spectral absorption lines named after the German physicist Joseph von Fraunhofer (1787–1826). The lines were originally observed as dark features (absorption lines) in the optical spectrum of the Sun.
**Free fall**- In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it.
**Frequency modulation**- Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing..
**Freezing point**- The
*melting point*(or, rarely,*liquefaction point*) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends on pressure and is usually specified at a standard pressure such as 1 atmosphere or 100 kPa.When considered as the temperature of the reverse change from liquid to solid, it is referred to as the*freezing point*or*crystallization point*. Because of the ability of substances to supercool, the freezing point can easily appear to be below its actual value. When the "characteristic freezing point" of a substance is determined, in fact the actual methodology is almost always "the principle of observing the disappearance rather than the formation of ice, that is, the melting point.^{[226]} **Friction**- Is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.
^{[227]}There are several types of friction:*Dry friction*is a force that opposes the relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into*static friction*("stiction") between non-moving surfaces, and*kinetic friction*between moving surfaces. With the exception of atomic or molecular friction, dry friction generally arises from the interaction of surface features, known as asperities (see Figure 1).*Fluid friction*describes the friction between layers of a viscous fluid that are moving relative to each other.^{[228]}^{[229]}

*Lubricated friction*is a case of fluid friction where a lubricant fluid separates two solid surfaces.^{[230]}^{[231]}^{[232]}

*Skin friction*is a component of drag, the force resisting the motion of a fluid across the surface of a body.*Internal friction*is the force resisting motion between the elements making up a solid material while it undergoes deformation.^{[229]}

**Function**- In mathematics, a function
^{[note 2]}is a binary relation between two sets that associates every element of the first set to exactly one element of the second set. Typical examples are functions from integers to integers, or from the real numbers to real numbers. **Fundamental frequency**- The fundamental frequency, often referred to simply as the
*fundamental*, is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids, the fundamental frequency is the lowest frequency sinusoidal in the sum of harmonically related frequencies, or the frequency of the difference between adjacent frequencies. In some contexts, the fundamental is usually abbreviated as, indicating the lowest frequency counting from zero.`f`_{0}^{[233]}^{[234]}^{[235]}In other contexts, it is more common to abbreviate it as, the first harmonic.`f`_{1}^{[236]}^{[237]}^{[238]}^{[239]}^{[240]}(The second harmonic is then`f`_{2}= 2⋅`f`_{1}, etc. In this context, the zeroth harmonic would be 0 Hz.) **Fundamental interaction**- In physics, the fundamental interactions, also known as
*fundamental forces*, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electromagnetic interactions, which produce significant long-range forces whose effects can be seen directly in everyday life, and the strong and weak interactions, which produce forces at minuscule, subatomic distances and govern nuclear interactions. Some scientists hypothesize that a fifth force might exist, but these hypotheses remain speculative.^{[241]}^{[242]}^{[243]} **Fundamental theorem of calculus**- Is a theorem that links the concept of differentiating a function with the concept of integrating a function.
**Fundamentals of Engineering Examination (US)**- The Fundamentals of Engineering (FE) exam, also referred to as the
*Engineer in Training*(*EIT*)*exam*, and formerly in some states as the*Engineering Intern*(*EI*)*exam*, is the first of two examinations that engineers must pass in order to be licensed as a Professional Engineer in the United States. The second examination is Principles and Practice of Engineering Examination. The FE exam is open to anyone with a degree in engineering or a related field, or currently enrolled in the last year of an ABET-accredited engineering degree program. Some state licensure boards permit students to take it prior to their final year, and numerous states allow those who have never attended an approved program to take the exam if they have a state-determined number of years of work experience in engineering. Some states allow those with ABET-accredited "Engineering Technology" or "ETAC" degrees to take the examination. The state of Michigan has no admission pre-requisites for the FE.^{[244]}The exam is administered by the National Council of Examiners for Engineering and Surveying (NCEES).

**Galvanic cell**- A galvanic cell or voltaic cell, named after Luigi Galvani or Alessandro Volta, respectively, is an electrochemical cell that derives electrical energy from spontaneous redox reactions taking place within the cell. It generally consists of two different metals immersed in electrolytes, or of individual half-cells with different metals and their ions in solution connected by a salt bridge or separated by a porous membrane. Volta was the inventor of the voltaic pile, the first electrical battery. In common usage, the word "battery" has come to include a single galvanic cell, but a battery properly consists of multiple cells.
^{[245]} **Gamma rays**- A gamma ray, or gamma radiation (symbol γ or \({\displaystyle \gamma }\)), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves and so imparts the highest photon energy.
**Gas**- Is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide). A gas mixture, such as air, contains a variety of pure gases. What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles.
**Gauge pressure**- Is zero-referenced against ambient air pressure, so it is equal to absolute pressure minus atmospheric pressure.
**Geiger counter**- Is an instrument used for detecting and measuring ionizing radiation. Also known as a
*Geiger–Muller counter*(or*Geiger–Müller counter*), it is widely used in applications such as radiation dosimetry, radiological protection, experimental physics, and the nuclear industry. **General relativity**- General relativity, also known as the
*general theory of relativity*, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the*curvature of spacetime*is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations. **Geometric mean**- In mathematics, the geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the
*n*th root of the product of n numbers, i.e., for a set of numbers*x*_{1},*x*_{2}, ...,*x*, the geometric mean is defined as_{n}- \({\displaystyle \left(\prod _{i=1}^{n}x_{i}\right)^{\frac {1}{n}}={\sqrt[{n}]{x_{1}x_{2}\cdots x_{n}}}}\)

- \({\displaystyle {{\mbox{Rate}}_{1} \over {\mbox{Rate}}_{2}}={\sqrt {M_{2} \over M_{1}}}}\),

- Rate
_{1}is the rate of effusion for the first gas. (volume or number of moles per unit time). - Rate
_{2}is the rate of effusion for the second gas.

*M*is the molar mass of gas 1_{1}*M*is the molar mass of gas 2._{2}

- \({\displaystyle U=-{\frac {GMm}{R}},}\)

- \({\displaystyle U=mgh}\)

**Half-life**- The period at which one-half of a quantity of an unstable isotope has decayed into other elements; the time at which half of a substance has diffused out of or otherwise reacted in a system.
**Haptic**- Tactile feedback technology using the operator's sense of touch. Also sometimes applied to robot manipulators with their own touch sensitivity.
**Hardness**- Is a measure of the resistance to localized plastic deformation induced by either mechanical indentation or abrasion. Some materials (e.g. metals) are harder than others (e.g. plastics, wood). Macroscopic hardness is generally characterized by strong intermolecular bonds, but the behavior of solid materials under force is complex; therefore, there are different measurements of hardness:
*scratch hardness*,*indentation hardness*, and*rebound hardness*. Hardness is dependent on ductility, elastic stiffness, plasticity, strain, strength, toughness, viscoelasticity, and viscosity. **Harmonic mean**- In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular, one of the Pythagorean means. Typically, it is appropriate for situations when the average of rates is desired.The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, and 4 is
- \({\displaystyle \left({\frac {1^{-1}+4^{-1}+4^{-1}}{3}}\right)^{-1}={\frac {3}{{\frac {1}{1}}+{\frac {1}{4}}+{\frac {1}{4}}}}={\frac {3}{1.5}}=2\,.}\)

- \({\displaystyle {\ce {pH}}={\ce {p}}K_{{\ce {a}}}+\log _{10}\left({\frac {[{\ce {Base}}]}{[{\ce {Acid}}]}}\right)}\)

**Ice point**- The freezing point of pure water at one atmosphere; 0°C (32°F).
^{[275]} **Ideal gas**- A model for gases that ignores inter-molecular forces. Most gases are approximately ideal at some high temperature and low pressure.
**Ideal gas constant**- The constant in the gas law that relates pressure, volume and temperature.
**Ideal gas law**- Also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law.
^{[276]}The ideal gas law is often written in an empirical form:- \({\displaystyle PV=nRT}\)

^{[277]}and Rudolf Clausius in 1857.^{[278]} **Identity**- In mathematics, an identity is an equality relating one mathematical expression
*A*to another mathematical expression*B*, such that*A*and*B*(which might contain some variables) produce the same value for all values of the variables within a certain range of validity.^{[279]}^{[280]}In other words,*A*=*B*is an identity if*A*and*B*define the same functions, and an identity is an equality between functions that are differently defined. For example, \({\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}}\) and \({\displaystyle \cos ^{2}\theta +\sin ^{2}\theta =1}\) are identities.^{[280]}Identities are sometimes indicated by the triple bar symbol ≡ instead of =, the equals sign.^{[281]} **Impedance (electrical)**- In electrical engineering, electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage is applied.
**Inclined plane**- Also known as a
*ramp*, is a flat supporting surface tilted at an angle, with one end higher than the other, used as an aid for raising or lowering a load.^{[282]}^{[283]}^{[284]}The inclined plane is one of the six classical simple machines defined by Renaissance scientists. Inclined planes are widely used to move heavy loads over vertical obstacles; examples vary from a ramp used to load goods into a truck, to a person walking up a pedestrian ramp, to an automobile or railroad train climbing a grade.^{[284]} **Indefinite integral**- A function whose derivative is a given function; an antiderivative.
^{[285]} **Inductance**- In electromagnetism and electronics, inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the current, and follows any changes in current. From Faraday's law of induction, any change in magnetic field through a circuit induces an electromotive force (EMF) (voltage) in the conductors, a process known as electromagnetic induction. This induced voltage created by the changing current has the effect of opposing the change in current. This is stated by Lenz's law, and the voltage is called
*back EMF*. Inductance is defined as the ratio of the induced voltage to the rate of change of current causing it. It is a proportionality factor that depends on the geometry of circuit conductors and the magnetic permeability of nearby materials.^{[286]}An electronic component designed to add inductance to a circuit is called an inductor. It typically consists of a coil or helix of wire. **Inductor**- An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it.
^{[287]}An inductor typically consists of an insulated wire wound into a coil. **Industrial engineering**- Is an engineering profession that is concerned with the optimization of complex processes, systems, or organizations by developing, improving and implementing integrated systems of people, money, knowledge, information and equipment. Industrial engineers use specialized knowledge and skills in the mathematical, physical and social sciences, together with the principles and methods of engineering analysis and design, to specify, predict, and evaluate the results obtained from systems and processes.
^{[288]}From these results, they are able to create new systems, processes or situations for the useful coordination of labour, materials and machines and also improve the quality and productivity of systems, physical or social.^{[289]} **Inertia**- Is the resistance of any physical object to any change in its velocity. This includes changes to the object's speed, or direction of motion. An aspect of this property is the tendency of objects to keep moving in a straight line at a constant speed, when no forces act upon them.
**Infrasound**- Infrasound, sometimes referred to as
*low-frequency sound*, describes sound waves with a frequency below the lower limit of audibility (generally 20 Hz). Hearing becomes gradually less sensitive as frequency decreases, so for humans to perceive infrasound, the sound pressure must be sufficiently high. The ear is the primary organ for sensing low sound, but at higher intensities it is possible to feel infrasound vibrations in various parts of the body. **Integral**- In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called
*integration*. Along with differentiation, integration is a fundamental operation of calculus,^{[b]}and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. **Integral transform**- In mathematics, an integral transform maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in the original function space. The transformed function can generally be mapped back to the original function space using the
*inverse transform*. **International System of Units**- The International System of Units (SI, abbreviated from the French
) is the modern form of the metric system. It is the only system of measurement with an official status in nearly every country in the world. It comprises a coherent system of units of measurement starting with seven base units, which are the second (the unit of time with the symbol s), metre (length, m), kilogram (mass, kg), ampere (electric current, A), kelvin (thermodynamic temperature, K), mole (amount of substance, mol), and candela (luminous intensity, cd). The system allows for an unlimited number of additional units, called derived units, which can always be represented as products of powers of the base units.*Système international (d'unités)*^{[Note 1]}Twenty-two derived units have been provided with special names and symbols.^{[Note 2]}The seven base units and the 22 derived units with special names and symbols may be used in combination to express other derived units,^{[Note 3]}which are adopted to facilitate measurement of diverse quantities. The SI system also provides twenty prefixes to the unit names and unit symbols that may be used when specifying power-of-ten (i.e. decimal) multiples and sub-multiples of SI units. The SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves. **Interval estimation**- In statistics, interval estimation is the use of sample data to calculate an interval of possible values of an unknown population parameter; this is in contrast to point estimation, which gives a single value. Jerzy Neyman (1937) identified interval estimation ("estimation by interval") as distinct from point estimation ("estimation by unique estimate"). In doing so, he recognized that then-recent work quoting results in the form of an estimate plus-or-minus a standard deviation indicated that interval estimation was actually the problem statisticians really had in mind.
**Inorganic chemistry**- Deals with synthesis and behavior of inorganic and organometallic compounds. This field covers chemical compounds that are not carbon-based, which are the subjects of organic chemistry. The distinction between the two disciplines is far from absolute, as there is much overlap in the subdiscipline of organometallic chemistry. It has applications in every aspect of the chemical industry, including catalysis, materials science, pigments, surfactants, coatings, medications, fuels, and agriculture.
^{[290]} **Ion**- Is a particle, atom or molecule with a net electrical charge. The charge of the electron is considered negative by convention. The negative charge of an ion is equal and opposite to charged proton(s) considered positive by convention. The net charge of an ion is non-zero due to its total number of electrons being unequal to its total number of protons.
**Ionic bonding**- Is a type of chemical bonding that involves the electrostatic attraction between oppositely charged ions, or between two atoms with sharply different electronegativities,
^{[291]}and is the primary interaction occurring in ionic compounds. It is one of the main types of bonding along with covalent bonding and metallic bonding. Ions are atoms (or groups of atoms) with an electrostatic charge. Atoms that gain electrons make negatively charged ions (called anions). Atoms that lose electrons make positively charged ions (called cations). This transfer of electrons is known as*electrovalence*in contrast to covalence. In the simplest case, the cation is a metal atom and the anion is a nonmetal atom, but these ions can be of a more complex nature, e.g. molecular ions like NH^{+}_{4}or SO^{2−}_{4}. In simpler words, an ionic bond results from the transfer of electrons from a metal to a non-metal in order to obtain a full valence shell for both atoms. **Ionization**- Ionization or
*ionisation*is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected. **Isotope**- Isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nucleon number. All isotopes of a given element have the same number of protons but different numbers of neutrons in each atom.
^{[292]}

**Joule**- The SI unit of energy.The joule, (symbol: J), is a derived unit of energy in the International System of Units.
^{[293]}It is equal to the energy transferred to (or work done on) an object when a force of one newton acts on that object in the direction of the force's motion through a distance of one metre (1 newton metre or N⋅m). It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).^{[294]}^{[295]}^{[296]}gh a conductor produces heat. **Joule heating**- Also known as resistive, resistance, or Ohmic heating, is the process by which the passage of an electric current through a conductor produces heat.

**Kalman filter**- In statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The Kalman filter has numerous applications in technology.
**Kelvin**- Is an absolute thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin (symbol: K) is the base unit of temperature in the International System of Units (SI).
**Kelvin–Planck statement**- (Or the
*Heat Engine Statement*), of the second law of thermodynamics states that*it is impossible to devise a cyclically operating heat engine, the effect of which is to absorb energy in the form of heat from a single thermal reservoir and to deliver an equivalent amount of work*.^{[297]}This implies that it is impossible to build a heat engine that has 100% thermal efficiency.^{[298]} **Kinematics**- Is a branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that caused the motion.
^{[299]}^{[300]}^{[301]}

**Laminar flow**- In fluid dynamics, laminar flow is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing.
^{[302]}At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids.^{[303]}In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface.^{[304]}Laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection. **Laplace transform**- In mathematics, the Laplace transform, named after its inventor Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function of a real variable \({\displaystyle t}\) (often time) to a function of a complex variable \({\displaystyle s}\) (complex frequency). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms differential equations into algebraic equations and convolution into multiplication.
^{[305]}^{[306]}^{[307]} **LC circuit**- A circuit consisting entirely of inductors (L) and capacitors (C).
**Le Chatelier's principle**- Le Chatelier's principle, also called
*Chatelier's principle*, is a principle of chemistry used to predict the effect of a change in conditions on chemical equilibria. The principle is named after French chemist Henry Louis Le Chatelier, and sometimes also credited to Karl Ferdinand Braun, who discovered it independently. It can be stated as:When any system at equilibrium for a long period of time is subjected to a change in concentration, temperature, volume, or pressure, (1) the system changes to a new equilibrium, and (2) this change partly counteracts the applied change.

It is common to treat the principle as a more general observation of systems,

^{[308]}such asWhen a settled system is disturbed, it will adjust to diminish the change that has been made to it

or, "roughly stated",

^{[308]}Any change in status quo prompts an opposing reaction in the responding system.

**Lenz's law**- Lenz's law, named after the physicist Emil Lenz who formulated it in 1834,
^{[309]}states that the direction of the electric current which is induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field.It is a qualitative law that specifies the direction of induced current, but states nothing about its magnitude. Lenz's law explains the direction of many effects in electromagnetism, such as the direction of voltage induced in an inductor or wire loop by a changing current, or the drag force of eddy currents exerted on moving objects in a magnetic field.Lenz's law may be seen as analogous to Newton's third law in classical mechanics.^{[310]} **Lepton**- In particle physics, a lepton is an elementary particle of half-integer spin (spin 1⁄2) that does not undergo strong interactions.
^{[311]}Two main classes of leptons exist: charged leptons (also known as the electron-like leptons), and neutral leptons (better known as neutrinos). Charged leptons can combine with other particles to form various composite particles such as atoms and positronium, while neutrinos rarely interact with anything, and are consequently rarely observed. The best known of all leptons is the electron. **Lever**- Is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge, or
*fulcrum*. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load and effort, the lever is divided into three types. Also, leverage is mechanical advantage gained in a system. It is one of the six simple machines identified by Renaissance scientists. A lever amplifies an input force to provide a greater output force, which is said to provide*leverage*. The ratio of the output force to the input force is the mechanical advantage of the lever. As such, the lever is a mechanical advantage device, trading off force against movement. **L'Hôpital's rule**- In mathematics, more specifically calculus, L'Hôpital's rule or L'Hospital's rule (French: [lopital],
English: /ˌloʊpiːˈtɑːl/,
*loh-pee-TAHL*) provides a technique to evaluate limits of indeterminate forms. Application (or repeated application) of the rule often converts an indeterminate form to an expression that can be easily evaluated by substitution. The rule is named after the 17th-century French mathematician Guillaume de l'Hôpital. Although the rule is often attributed to L'Hôpital, the theorem was first introduced to him in 1694 by the Swiss mathematician Johann Bernoulli.L'Hôpital's rule states that for functions f and g which are differentiable on an open interval I except possibly at a point c contained in I, if \({\displaystyle \lim _{x\to c}f(x)=\lim _{x\to c}g(x)=0{\text{ or }}\pm \infty ,}\) and \({\displaystyle g'(x)\neq 0}\) for all x in I with*x*≠*c*, and \({\displaystyle \lim _{x\to c}{\frac {f'(x)}{g'(x)}}}\) exists, then- \({\displaystyle \lim _{x\to c}{\frac {f(x)}{g(x)}}=\lim _{x\to c}{\frac {f'(x)}{g'(x)}}.}\)

**Light**- Light or
*visible light*is electromagnetic radiation within the portion of the electromagnetic spectrum that can be perceived by the human eye.^{[312]}Visible light is usually defined as having wavelengths in the range of 400–700 nm, between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths).^{[313]}^{[314]}This wavelength means a frequency range of roughly 430–750 terahertz (THz). **Linear actuator**- Is an actuator that creates motion in a straight line, in contrast to the circular motion of a conventional electric motor. Linear actuators are used in machine tools and industrial machinery, in computer peripherals such as disk drives and printers, in valves and dampers, and in many other places where linear motion is required. Hydraulic or pneumatic cylinders inherently produce linear motion. Many other mechanisms are used to generate linear motion from a rotating motor.
**Linear algebra**- The mathematics of equations where the unknowns are only in the first power.
**Linear elasticity**- Is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics.
**Liquid**- A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, and plasma), and is the only state with a definite volume but no fixed shape. A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena. Water is, by far, the most common liquid on Earth.
**Logarithm**- In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the
*base*b, must be raised, to produce that number x. In the simplest case, the logarithm counts the number of occurrences of the same factor in repeated multiplication; e.g., since 1000 = 10 × 10 × 10 = 10^{3}, the "logarithm base 10" of 1000 is 3, or log_{10}(1000) = 3. The logarithm of x to*base*b is denoted as log_{b}(*x*), or without parentheses, log_{b}*x*, or even without the explicit base, log*x*, when no confusion is possible, or when the base does not matter such as in big O notation.More generally, exponentiation allows any positive real number as base to be raised to any real power, always producing a positive result, so log_{b}(*x*) for any two positive real numbers b and x, where b is not equal to 1, is always a unique real number y. More explicitly, the defining relation between exponentiation and logarithm is:- \({\displaystyle \log _{b}(x)=y\ }\) exactly if \({\displaystyle \ b^{y}=x\ }\) and \({\displaystyle \ x>0}\) and \({\displaystyle \ b>0}\) and \({\displaystyle \ b\neq 1}\).

_{2}64 = 6, as 2^{6}= 64.The logarithm base 10 (that is*b*= 10) is called the decimal or common logarithm and is commonly used in science and engineering. The natural logarithm has the number e (that is*b*≈ 2.718) as its base; its use is widespread in mathematics and physics, because of its simpler integral and derivative. The binary logarithm uses base 2 (that is*b*= 2) and is frequently used in computer science. Logarithms are examples of concave functions.^{[315]} **Logarithmic identities**- Several important formulas, sometimes called logarithmic identities or
*log laws*, relate logarithms to one another.^{[316]} **Logarithmic mean temperature difference**- (Also known as log mean temperature difference, LMTD) is used to determine the temperature driving force for heat transfer in flow systems, most notably in heat exchangers. The LMTD is a logarithmic average of the temperature difference between the hot and cold feeds at each end of the double pipe exchanger. For a given heat exchanger with constant area and heat transfer coefficient, the larger the LMTD, the more heat is transferred. The use of the LMTD arises straightforwardly from the analysis of a heat exchanger with constant flow rate and fluid thermal properties.
**Lumped capacitance model**- A lumped-capacitance model, also called
*lumped system analysis*,^{[317]}reduces a thermal system to a number of discrete “lumps” and assumes that the temperature difference inside each lump is negligible. This approximation is useful to simplify otherwise complex differential heat equations. It was developed as a mathematical analog of electrical capacitance, although it also includes thermal analogs of electrical resistance as well. **Lumped element model**- The lumped-element model (also called
*lumped-parameter model*, or*lumped-component model*) simplifies the description of the behaviour of spatially distributed physical systems into a topology consisting of discrete entities that approximate the behaviour of the distributed system under certain assumptions. It is useful in electrical systems (including electronics), mechanical multibody systems, heat transfer, acoustics, etc. Mathematically speaking, the simplification reduces the state space of the system to a finite dimension, and the partial differential equations (PDEs) of the continuous (infinite-dimensional) time and space model of the physical system into ordinary differential equations (ODEs) with a finite number of parameters.

**Macaulay's method****(The double integration method)**is a technique used in structural analysis to determine the deflection of Euler-Bernoulli beams. Use of Macaulay’s technique is very convenient for cases of discontinuous and/or discrete loading. Typically partial uniformly distributed loads (u.d.l.) and uniformly varying loads (u.v.l.) over the span and a number of concentrated loads are conveniently handled using this technique.**Mach number**- The ratio of the speed of an object to the speed of sound..
**Machine**- A machine (or mechanical device) is a mechanical structure that uses power to apply forces and control movement to perform an intended action. Machines can be driven by animals and people, by natural forces such as wind and water, and by chemical, thermal, or electrical power, and include a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement. They can also include computers and sensors that monitor performance and plan movement, often called mechanical systems.
**Machine code**- In computer programming, machine code, consisting of machine language instructions, is a low-level programming language used to directly control a computer's central processing unit (CPU). Each instruction causes the CPU to perform a very specific task, such as a load, a store, a jump, or an arithmetic logic unit (ALU) operation on one or more units of data in the CPU's registers or memory.
**Machine element**- .
**Machine learning**- .
**Maclaurin series**- .
**Magnetic field**- .
**Magnetism**- .
**Manufacturing engineering**- .
**Mass balance**- .
**Mass density**- .
**Mass moment of inertia**- .
**Mass number**- .
**Mass spectrometry**- .
**Material failure theory**- .
**Material properties**- .
**Materials science**- .
**Mathematical optimization**- .
**Mathematical physics**- .
**Mathematics**- .
**Matrix**- .
**Matter**- .
**Maximum-distortion energy theory**- .
**Maximum-normal-stress theory**- .
**Maximum shear stress**- .
**Maxwell's equations**- A number of basic laws describing the behavior of electric current and potential.
**Mean**- .
**Measures of central tendency**- .
**Mechanical advantage**- .
**Mechanical engineering**- .
**Mechanical filter**- .
**Mechanical wave**- .
**Mechanics**- .
**Mechanism**- .
**Median**- .
**Melting**- .
**Melting point**- .
**Meson**- .
**Metal alloy**- .
**Metallic bond**- .
**Middle-out**- A combination of top-down and bottom-up design.
^{[318]} **Mid-range**- .
**Midhinge**- .
**Mining engineering**- .
**Miller indices**- .
**Mobile robot**- .
**Mode**- .
**Modulus of elasticity**- .
**Mohr's circle**- A graphical method of analyzing the three-dimensional stresses in a system that has a loading force applied to it.
**Molality**- .
**Molar concentration**- .
**Molar absorptivity**- .
**Molar mass**- .
**Molarity**- .
**Molding**- .
**Molecule**- .
**Molecular physics**- .
**Moment of inertia**- .
**Multibody system**- .
**Multidisciplinary design optimization**- .
**Mutual inductance**- .
**Muon**- .

**Nanoengineering**- Is the practice of engineering on the nanoscale. It derives its name from the nanometre, a unit of measurement equalling one billionth of a meter. Nanoengineering is largely a synonym for nanotechnology, but emphasizes the engineering rather than the pure science aspects of the field.
**Nanotechnology**- The technology of systems built with moving parts on the order of a nanometre in size.
- In physics, the Navier–Stokes equations are a set of partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician George Gabriel Stokes.
**Neutrino**- A neutrino (denoted by the Greek letter ν) is a fermion (an elementary particle with spin of 1/2) that interacts only via the weak subatomic force and gravity.
^{[319]}^{[320]}The neutrino is so named because it is electrically neutral and because its rest mass is so small (*-ino*) that it was long thought to be zero. The mass of the neutrino is much smaller than that of the other known elementary particles.^{[321]}The weak force has a very short range, the gravitational interaction is extremely weak, and neutrinos do not participate in the strong interaction.^{[322]}Thus, neutrinos typically pass through normal matter unimpeded and undetected.^{[323]}^{[320]} **Newtonian fluid**- Is a fluid in which the viscous stresses arising from its flow, at every point, are linearly
^{[324]}correlated to the local strain rate—the rate of change of its deformation over time.^{[325]}^{[326]}^{[327]}That is equivalent to saying those forces are proportional to the rates of change of the fluid's velocity vector as one moves away from the point in question in various directions. More precisely, a fluid is Newtonian only if the tensors that describe the viscous stress and the strain rate are related by a constant viscosity tensor that does not depend on the stress state and velocity of the flow. If the fluid is also isotropic (that is, its mechanical properties are the same along any direction), the viscosity tensor reduces to two real coefficients, describing the fluid's resistance to continuous shear deformation and continuous compression or expansion, respectively. **Norton's theorem**- In direct-current circuit theory, Norton's theorem (aka
*Mayer–Norton theorem*) is a simplification that can be applied to networks made of linear time-invariant resistances, voltage sources, and current sources. At a pair of terminals of the network, it can be replaced by a current source and a single resistor in parallel. For alternating current (AC) systems the theorem can be applied to reactive impedances as well as resistances. **Nozzle**- Is a device designed to control the direction or characteristics of a fluid flow (especially to increase velocity) as it exits (or enters) an enclosed chamber or pipe. A nozzle is often a pipe or tube of varying cross sectional area, and it can be used to direct or modify the flow of a fluid (liquid or gas). Nozzles are frequently used to control the rate of flow, speed, direction, mass, shape, and/or the pressure of the stream that emerges from them. In a nozzle, the velocity of fluid increases at the expense of its pressure energy.
*n*th root- To put a number of function to the exponential power of 1/n.
**Nuclear binding energy**- The difference between the total mass energy of a nucleus and the mass energy of the isolated nucleons.
**Nuclear engineering**- The profession that deals with nuclear power.
**Nuclear fusion**- Is a reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles (neutrons or protons). The difference in mass between the reactants and products is manifested as either the release or the absorption of energy. This difference in mass arises due to the difference in atomic binding energy between the nuclei before and after the reaction. Fusion is the process that powers active or main sequence stars and other high-magnitude stars, where large amounts of energy are released.
**Nuclear physics**- The science that describes the components of atoms.
**Nuclear potential energy**- The energy that is given up in decay of an unstable nucleus.
**Nuclear power**- The use of energy derived from nuclear chain reactions for electricity production or ship propulsion.

**Ohm**- The SI unit of electrical resistance.
**Ohm's law**- A law describing the relationship between resistance, current, and voltage.
**Optics**- The study of light.
**Organic chemistry**- The study of carbon compounds.
**Osmosis**- The spontaneous movement of molecules or ions through a semi-permable membrane, tending to equalize concentration on both sides.

**Parallel circuit**- A circuit that begins and ends at the same node as another circuit.
**Parity (mathematics)**- In mathematics, parity is the property of an integer of whether it is even or odd. An integer's parity is even if it is divisible by two with no remainders left and its parity is odd if its remainder is 1.
^{[328]}For example, -4, 0, 82, and 178 are even because there is no remainder when dividing it by 2. By contrast, -3, 5, 7, 21 are odd numbers as they leave a remainder of 1 when divided by 2. **Parity (physics)**- .In quantum mechanics, a parity transformation (also called parity inversion) is the flip in the sign of
*one*spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point reflection):- \({\displaystyle \mathbf {P} :{\begin{pmatrix}x\\y\\z\end{pmatrix}}\mapsto {\begin{pmatrix}-x\\-y\\-z\end{pmatrix}}.}\)

**P**(in any number of dimensions) has determinant equal to −1, and hence is distinct from a rotation, which has a determinant equal to 1. In a two-dimensional plane, a simultaneous flip of all coordinates in sign is*not*a parity transformation; it is the same as a 180°-rotation.In quantum mechanics, wave functions that are unchanged by a parity transformation are described as even functions, while those that change sign under a parity transformation are odd functions.fn=A hydrocarbon compound, solid at room temperature. **Paramagnetism**- Is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, diamagnetic materials are repelled by magnetic fields and form induced magnetic fields in the direction opposite to that of the applied magnetic field.
^{[329]}Paramagnetic materials include most chemical elements and some compounds;^{[330]}they have a relative magnetic permeability slightly greater than 1 (i.e., a small positive magnetic susceptibility) and hence are attracted to magnetic fields. The magnetic moment induced by the applied field is linear in the field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect and modern measurements on paramagnetic materials are often conducted with a SQUID magnetometer. **Particle accelerator**- Is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams.
^{[331]} **Particle displacement**- Particle displacement or displacement amplitude is a measurement of distance of the movement of a sound particle from its equilibrium position in a medium as it transmits a sound wave.
^{[332]}The SI unit of particle displacement is the metre (m). In most cases this is a longitudinal wave of pressure (such as sound), but it can also be a transverse wave, such as the vibration of a taut string. In the case of a sound wave travelling through air, the particle displacement is evident in the oscillations of air molecules with, and against, the direction in which the sound wave is travelling.^{[333]} **Particle physics**- Particle physics (also known as
*high energy physics*) is a branch of physics that studies the nature of the particles that constitute matter and radiation. Although the word*particle*can refer to various types of very small objects (e.g. protons, gas particles, or even household dust),*particle physics*usually investigates the irreducibly smallest detectable particles and the fundamental interactions necessary to explain their behaviour. In current understanding, these elementary particles are excitations of the quantum fields that also govern their interactions. The currently dominant theory explaining these fundamental particles and fields, along with their dynamics, is called the Standard Model. Thus, modern particle physics generally investigates the Standard Model and its various possible extensions, e.g. to the newest "known" particle, the Higgs boson, or even to the oldest known force field, gravity.^{[334]}^{[335]} **Pascal's law**- Pascal's law (also
*Pascal's principle*^{[336]}^{[337]}^{[338]}or the*principle of transmission of fluid-pressure*) is a principle in fluid mechanics that states that a pressure change occurring anywhere in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere.^{[339]}The law was established by French mathematician Blaise Pascal^{[30]}in 1647–48.^{[340]} **Pendulum**- Is a weight suspended from a pivot so that it can swing freely.
^{[341]}When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing. **Petroleum engineering**- Is a field of engineering concerned with the activities related to the production of Hydrocarbons, which can be either crude oil or natural gas.
^{[342]}Exploration and production are deemed to fall within the*upstream*sector of the oil and gas industry. Exploration, by earth scientists, and petroleum engineering are the oil and gas industry's two main subsurface disciplines, which focus on maximizing economic recovery of hydrocarbons from subsurface reservoirs. Petroleum geology and geophysics focus on provision of a static description of the hydrocarbon reservoir rock, while petroleum engineering focuses on estimation of the recoverable volume of this resource using a detailed understanding of the physical behavior of oil, water and gas within porous rock at very high pressure. **pH**- A logarithmic measure of the concentration of hydrogen ions in an acid or base solution.
**Phase (matter)**- .
**Phase (waves)**- .
**Phase diagram**- .
**Phase equilibrium**- .
**Photon**- A particle with no rest mass that carries electromagnetic energy.
**Physical chemistry**- .
**Physical quantity**- .
**Physics**- .
**Planck constant**- .
**Plasma physics**- .
**Plasticity**- .
**Pneumatics**- The control of mechanical force and movement, generated by the application of compressed gas.
**Point estimation**- .
**Polyphase system**- An electrical system that uses a set of alternating currents at different phases.
**Power (electric)**- .
**Power (physics)**- .
**Power factor**- .
**Pressure**- The force per unit area .
**Probability**- .
**Probability distribution**- .
**Probability theory**- .
**Psi particle**- .
**Pulley**- .
**Pump**- .

**Quantum electrodynamics**- In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.
**Quantum field theory**- In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity and quantum mechanics,
^{[343]}^{:xi}but*not*general relativity's description of gravity. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. **Quantum mechanics**- Is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.
^{[344]}^{:1.1}It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.

**Regelation**- The phenomena of melting under pressure, then freezing when the pressure is reduced.
**Relative density**- Relative density, or specific gravity,
^{[345]}^{[346]}is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest (at 4 °C or 39.2 °F); for gases, the reference is air at room temperature (20 °C or 68 °F). The term "relative density" is often preferred in scientific usage. **Relative velocity**- The
*relative velocity*\({\displaystyle {\vec {v}}_{B\mid A}}\) (also \({\displaystyle {\vec {v}}_{BA}}\) or \({\displaystyle {\vec {v}}_{B\operatorname {rel} A}}\)) is the velocity of an object or observer**B**in the rest frame of another object or observer**A**. **Reliability engineering**- Is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specified period of time.
^{[347]}Reliability is closely related to availability, which is typically described as the ability of a component or system to function at a specified moment or interval of time. **Resistivity**- Electrical resistivity (also called specific electrical resistance or volume resistivity) and its inverse, electrical conductivity, is a fundamental property of a material that quantifies how strongly it resists or conducts electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter
*ρ*(rho). The SI unit of electrical resistivity is the ohm-meter (Ω⋅m).^{[348]}^{[349]}^{[350]}For example, if a 1 m × 1 m × 1 m solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is 1 Ω, then the resistivity of the material is 1 Ω⋅m. **Resistor**- Is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat, may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements (such as a volume control or a lamp dimmer), or as sensing devices for heat, light, humidity, force, or chemical activity.
**Reynolds number**- The Reynolds number (Re) helps predict flow patterns in different fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. Reynolds numbers are an important dimensionless quantity in fluid mechanics.
**Rheology**- Is the study of the flow of matter, primarily in a liquid or gas state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force. Rheology is a branch of physics, and it is the science that deals with the deformation and flow of materials, both solids and liquids.
^{[351]} **Rigid body**- In physics, a rigid body (also known as a
*rigid object*^{[352]}) is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass. In the study of special relativity, a perfectly rigid body does not exist; and objects can only be assumed to be rigid if they are not moving near the speed of light. In quantum mechanics, a rigid body is usually thought of as a collection of point masses. For instance, molecules (consisting of the point masses: electrons and nuclei) are often seen as rigid bodies (see classification of molecules as rigid rotors). **Robonaut**- A development project conducted by NASA to create humanoid robots capable of using space tools and working in similar environments to suited astronauts..
**Robotics**- Is an interdisciplinary field that integrates computer science and engineering.
^{[353]}Robotics involves design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist humans. Robotics integrates fields of mechanical engineering, electrical engineering, information engineering, mechatronics, electronics, bioengineering, computer engineering, control engineering, software engineering, among others. **Root mean square**- In mathematics and its applications, the root mean square (RMS or rms) is defined as the square root of the mean square (the arithmetic mean of the squares of a set of numbers).
^{[354]}The RMS is also known as the*quadratic mean*^{[355]}^{[356]}and is a particular case of the generalized mean with exponent 2. RMS can also be defined for a continuously varying function in terms of an integral of the squares of the instantaneous values during a cycle. For alternating electric current, RMS is equal to the value of the constant direct current that would produce the same power dissipation in a resistive load.^{[354]}In estimation theory, the root-mean-square deviation of an estimator is a measure of the imperfection of the fit of the estimator to the data. **Root-mean-square speed**- In the physics of gas molecules, the root-mean-square speed is defined as the square root of the average squared-speed. The RMS speed of an ideal gas is calculated using the following equation:
- \({\displaystyle v_{\text{RMS}}={\sqrt {3RT \over M}}}\)

*R*represents the gas constant, 8.314 J/(mol·K),*T*is the temperature of the gas in kelvins, and*M*is the molar mass of the gas in kilograms per mole. In physics, speed is defined as the scalar magnitude of velocity. For a stationary gas, the average speed of its molecules can be in the order of thousands of km/hr, even though the average velocity of its molecules is zero. **Rotational energy**- Rotational energy or
*angular kinetic energy*is kinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational energy separately around an object's axis of rotation, the following dependence on the object's moment of inertia is observed:- \({\displaystyle E_{\mathrm {rotational} }={\frac {1}{2}}I\omega ^{2}}\)

- \({\displaystyle \omega \ }\) is the angular velocity
- \({\displaystyle I\ }\) is the moment of inertia around the axis of rotation
- \({\displaystyle E\ }\) is the kinetic energy

- \({\displaystyle v=2\pi r\omega _{\text{cyc}}}\)

- \({\displaystyle v=r\omega _{\text{rad}}}\)

- \({\displaystyle \omega _{\text{cyc}}=v/2\pi r}\)

- \({\displaystyle \omega _{\text{rad}}=v/r}\)

- \({\displaystyle \omega _{\text{cyc}}=\omega _{\text{rad}}/2\pi \,}\)

- \({\displaystyle \omega _{\text{cyc}}=\omega _{\text{deg}}/360\,}\)

- \({\displaystyle \omega _{\text{cyc}}\,}\) is rotational speed in cycles per second
- \({\displaystyle \omega _{\text{rad}}\,}\) is angular speed in radians per second
- \({\displaystyle \omega _{\text{deg}}\,}\) is angular speed in degrees per second

**Safe failure fraction (SFF)**- A term used in functional safety for the proportion of failures that are either non-hazardous or detected automatically. The opposite of SFF is the proportion of undetected, hazardous failures.
^{[359]} **Safety data sheet**- A safety data sheet (SDS),
^{[360]}material safety data sheet (MSDS), or product safety data sheet (PSDS) are documents that list information relating to occupational safety and health for the use of various substances and products. SDSs are a widely used system for cataloguing information on chemicals, chemical compounds, and chemical mixtures. SDS information may include instructions for the safe use and potential hazards associated with a particular material or product, along with spill-handling procedures. The older MSDS formats could vary from source to source within a country depending on national requirements; however, the newer SDS format is internationally standardized. **Sanitary engineering**- Sanitary engineering, also known as public health engineering or wastewater engineering, is the application of engineering methods to improve sanitation of human communities, primarily by providing the removal and disposal of human waste, and in addition to the supply of safe potable water.
**Saturated compound**- In chemistry, a saturated compound is a chemical compound (or ion) that resists the addition reactions, such as hydrogenation, oxidative addition, and binding of a Lewis base. The term is used in many contexts and for many classes of chemical compounds. Overall, saturated compounds are less reactive than unsaturated compounds. Saturation is derived from the Latin word
*saturare*, meaning 'to fill')^{[361]} **Scalar (mathematics)**- .
**Scalar (physics)**- .
**Scalar multiplication**- .
**Screw**- .
**Series circuit**- An electrical circuit in which the same current passes through each component, with only one path.
**Servo**- A motor that moves to and maintains a set position under command, rather than continuously moving.
**Servomechanism**- An automatic device that uses error-sensing negative feedback to correct the performance of a mechanism.
**Shadow matter**- In physics, mirror matter, also called shadow matter or Alice matter, is a hypothetical counterpart to ordinary matter.
^{[362]} **Shear flow**- .
**Shear strength**- .
**Shear stress**- .
**Shortwave radiation**- .
**SI units**- .
**Signal processing**- .
**Simple machine**- A mechanical device that changes the direction or magnitude of a force.
**Siphon**- A closed tube that conveys liquids between two levels without pumping.
**Solid mechanics**- .
**Solid-state physics**- .
**Solid solution strengthening**- .
**Solubility**- .
**Solubility equilibrium**- .
**Sound**- .
**Special relativity**- .
**Specific heat**- The amount of energy required to change the temperature of a unit mass of substance by one degree.
**Specific gravity**- The ratio between the mass density of a substance to that of water.
**Specific volume**- The volume of a unit mass of a substance.
**Specific weight**- The weight of a substance per unit volume.
**Spontaneous combustion**- .
**Stagnation pressure**- .
**Standard electrode potential**- .
**State of matter**- .
**Statics**- The study of forces in a non-moving, rigid body.
**Statistics**- .
**Steam table**- .
**Stefan–Boltzmann law**- .
**Stewart platform**- a movable platform using six linear actuators, hence also known as a Hexapod.
**Stiffness**- .
**Stoichiometry**- .
**Strain**- .
**Strain hardening**- .
**Strength of materials**- .
**Stress**- .
**Stress–strain analysis**- .
**Stress–strain curve**- .
**Structural analysis**- .
**Structural load**- .
**Sublimation**- .
**Subsumption architecture**- a robot architecture that uses a modular, bottom-up design beginning with the least complex behavioral tasks.
**Surface tension**- .
**Superconductor**- .
**Superhard material**- .
**Supersaturation**- .
**Surgical robot**- a remote manipulator used for keyhole surgery.

**Tangential acceleration**- .
**Technical standard**- A technical standard is an established norm or requirement for a repeatable technical task. It is usually a formal document that establishes uniform engineering or technical criteria, methods, processes, and practices. In contrast, a custom, convention, company product, corporate standard, and so forth that becomes generally accepted and dominant is often called a
*de facto*standard. **Temperature**- Is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy, when a body is in contact with another that is colder. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have used various reference points and thermometric substances for definition. The most common scales are the Celsius scale (formerly called
*centigrade*, denoted °C), the Fahrenheit scale (denoted °F), and the Kelvin scale (denoted K), the last of which is predominantly used for scientific purposes by conventions of the International System of Units (SI). **Tempering (metallurgy)**- Heat treatment to alter the crystal structure of a metal such as steel.
**Tensile force**- Pulling force, tending to lengthen an object.
**Tensile modulus**- .
**Tensile strength**- Ultimate tensile strength (UTS), often shortened to tensile strength (TS), ultimate strength, or \({\displaystyle F_{\text{tu}}}\) within equations,
^{[363]}^{[364]}^{[365]}is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials the ultimate tensile strength is close to the yield point, whereas in ductile materials the ultimate tensile strength can be higher. **Tensile testing**- Tensile testing, also known as tension testing,
^{[366]}is a fundamental materials science and engineering test in which a sample is subjected to a controlled tension until failure. Properties that are directly measured via a tensile test are ultimate tensile strength, breaking strength, maximum elongation and reduction in area.^{[367]}From these measurements the following properties can also be determined: Young's modulus, Poisson's ratio, yield strength, and strain-hardening characteristics.^{[368]}*Uniaxial tensile testing*is the most commonly used for obtaining the mechanical characteristics of isotropic materials. Some materials use*biaxial tensile testing*. The main difference between these testing machines being how load is applied on the materials. **Tension member**- Tension members are structural elements that are subjected to axial tensile forces. Examples of tension members are bracing for buildings and bridges, truss members, and cables in suspended roof systems.
**Thermal conduction**- .
**Thermal equilibrium**- .
**Thermal radiation**- .
**Thermodynamics**- The science of the flow of heat.
**Theory of relativity**- .
**Thévenin's theorem**- .
**Three-phase**- Electric power using three alternating currents, displaced in time.
**Torque**- Twisting force.
**Torsional vibration**- .
**Toughness**- .
**Trajectory**- .
**Transducer**- .
**Transformer**- .
**Trigonometric functions**- .
**Trigonometry**- .
**Trimean**- The
**trimean**is a measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles **Triple point**- .
**Trouton's rule**- .
**Truncated mean**- .
**Truss**- .
**Turbine**- .
**Turbomachinery**- .
**Turbulence**- .

**Ultimate tensile strength****Ultimate tensile strength**(**UTS**), often shortened to**tensile strength**(**TS**),**ultimate strength**, or**Ftu**within equations,^{[363]}^{[364]}^{[365]}is the capacity of a material or structure to withstand loads tending to elongate, as opposed to compressive strength, which withstands loads tending to reduce size. In other words, tensile strength resists tension (being pulled apart), whereas compressive strength resists compression (being pushed together). Ultimate tensile strength is measured by the maximum stress that a material can withstand while being stretched or pulled before breaking. In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently.**Uncertainty principle**- In quantum mechanics, the
**uncertainty principle**(also known as**Heisenberg's uncertainty principle**) is any of a variety of mathematical inequalities^{[369]}asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position*x*and momentum*p*, can be known. **Unicode**- A standard for the consistent encoding of textual characters.
**Unit vector**- In mathematics, a
**unit vector**in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat": \({\displaystyle {\hat {\imath }}}\) (pronounced "i-hat"). The term direction vector is used to describe a unit vector being used to represent spatial direction, and such quantities are commonly denoted as**d**. . **Unsaturated compound**- .
**Upthrust**- Buoyancy, or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. The pressure difference results in a net upward force on the object. The magnitude of the force is proportional to the pressure difference, and (as explained by Archimedes' principle) is equivalent to the weight of the fluid that would otherwise occupy the submerged volume of the object, i.e. the displaced fluid.
**Utility frequency**- The utility frequency, (power) line frequency (American English) or mains frequency (British English) is the nominal frequency of the oscillations of alternating current (AC) in a wide area synchronous grid transmitted from a power station to the end-user. In large parts of the world this is 50 Hz, although in the Americas and parts of Asia it is typically 60 Hz. Current usage by country or region is given in the list of mains electricity by country.

**Vacuole**- Is a membrane-bound organelle which is present in plant and fungal cells and some protist, animal
^{[370]}and bacterial cells.^{[371]}Vacuoles are essentially enclosed compartments which are filled with water containing inorganic and organic molecules including enzymes in solution, though in certain cases they may contain solids which have been engulfed. Vacuoles are formed by the fusion of multiple membrane vesicles and are effectively just larger forms of these.^{[372]}The organelle has no basic shape or size; its structure varies according to the requirements of the cell. **Vacuum**- An absence of mass in a volume.
**Valence**- In chemistry, the
**valence**or**valency**of an element is a measure of its combining power with other atoms when it forms chemical compounds or molecules. The concept of valence developed in the second half of the 19th century and helped successfully explain the molecular structure of inorganic and organic compounds.^{[373]}The quest for the underlying causes of valence led to the modern theories of chemical bonding, including the cubical atom (1902), Lewis structures (1916), valence bond theory (1927), molecular orbitals (1928), valence shell electron pair repulsion theory (1958), and all of the advanced methods of quantum chemistry. **Valence band**- In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level and thus determine the electrical conductivity of the solid. In non-metals, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states. On a graph of the electronic band structure of a material, the valence band is located below the Fermi level, while the conduction band is located above it. The distinction between the valence and conduction bands is meaningless in metals, because conduction occurs in one or more partially filled bands that take on the properties of both the valence and conduction bands.
**Valence bond theory**- In chemistry, valence bond (VB) theory is one of the two basic theories, along with molecular orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine to give individual chemical bonds when a molecule is formed. In contrast, molecular orbital theory has orbitals that cover the whole molecule.
^{[374]} **Valence electron**- In chemistry and physics, a valence electron is an outer shell electron that is associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed; in a single covalent bond, both atoms in the bond contribute one valence electron in order to form a shared pair.
**Valence shell**- The valence shell is the set of orbitals which are energetically accessible for accepting electrons to form chemical bonds. For main group elements, the valence shell consists of the ns and np orbitals in the outermost electron shell. In the case of transition metals (the (n-1)d orbitals), and lanthanides and actinides (the (n-2)f and (n-1)d orbitals), the orbitals involved can also be in an inner electron shell. Thus, the
*shell*terminology is a misnomer as there is no correspondence between the valence shell and any particular electron shell in a given element. A scientifically correct term would be*valence orbital*to refer to the energetically accessible orbitals of an element. **Valve**- Is a device or natural object that regulates, directs or controls the flow of a fluid (gases, liquids, fluidized solids, or slurries) by opening, closing, or partially obstructing various passageways. Valves are technically fittings, but are usually discussed as a separate category. In an open valve, fluid flows in a direction from higher pressure to lower pressure. The word is derived from the Latin
*valva*, the moving part of a door, in turn from*volvere*, to turn, roll. **van der Waals equation**- .
**van der Waals force**- In molecular physics, the Van der Waals force, named after Dutch physicist Johannes Diderik van der Waals, is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and therefore more susceptible to disturbance. The Van der Waals force quickly vanishes at longer distances between interacting molecules.
**van 't Hoff equation**- .
**van 't Hoff factor**- .
**Variable capacitor**- .
**Variable resistor**- .
**Vector space**- .
**Venturi effect**- .
**Vibration**- .
**Virtual leak**- Traces of gas trapped in cavities within a vacuum chamber, slowly dissipating out in the main chamber, thus appearing like a leak from the outside.
**Viscoelasticity**- .
**Viscosity**- The
**viscosity**of a fluid is the measure of its resistance to gradual deformation by shear stress or tensile stress.^{[375]}For liquids, it corresponds to the informal concept of "thickness": for example, honey has a higher viscosity than water.^{[376]} **Volt-ampere**- (VA), is the unit used for the apparent power in an electrical circuit. The apparent power equals the product of root-mean-square (RMS) voltage and RMS current.
^{[377]}In direct current (DC) circuits, this product is equal to the real power (active power)^{[378]}in watts. Volt-amperes are useful only in the context of alternating current (AC) circuits. The volt-ampere is dimensionally equivalent to the watt (in SI units, 1 VA = 1 N m A^{−1}s^{−1}A = 1 N m s^{−1}= 1 J s^{−1}= 1 W). VA rating is most useful in rating wires and switches (and other power handling equipment) for inductive loads. **Volt-ampere reactive**- .
**Volta potential**- The
**Volta potential**(also called**Volta potential difference**,**contact potential difference**,**outer potential difference**, Δψ, or "delta psi") in electrochemistry, is the electrostatic potential difference between two metals (or one metal and one electrolyte) that are in contact and are in thermodynamic equilibrium. Specifically, it is the potential difference between a point close to the surface of the first metal, and a point close to the surface of the second metal (or electrolyte).^{[379]} **Voltage****Voltage**,**electric potential difference**,**electric pressure**or**electric tension**is the difference in electric potential between two points. The difference in electric potential between two points (i.e., voltage) is defined as the work needed per unit of charge against a static electric field to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named*volt*.^{[380]}In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule (of work) per 1 coulomb (of charge). The official SI definition for*volt*uses power and current, where 1 volt = 1 watt (of power) per 1 ampere (of current).^{[380]}**Volumetric flow rate**- Also known as
**volume flow rate**,**rate of fluid flow**or**volume velocity**, is the volume of fluid which passes per unit time; usually represented by the symbol Q (sometimes V̇). The SI unit is m^{3}/s (cubic metres per second). **von Mises yield criterion**- The
**von Mises yield criterion**(also known as the maximum distortion energy criterion^{[381]}) suggests that yielding of a ductile material begins when the second deviatoric stress invariant \({\displaystyle J_{2}}\) reaches a critical value.^{[382]}It is part of plasticity theory that applies best to ductile materials, such as some metals. Prior to yield, material response can be assumed to be of a nonlinear elastic, viscoelastic, or linear elastic behavior.In materials science and engineering the von Mises yield criterion can also be formulated in terms of the**von Mises stress**or**equivalent tensile stress**, \({\displaystyle \sigma _{v}}\). This is a scalar value of stress that can be computed from the Cauchy stress tensor. In this case, a material is said to start yielding when the von Mises stress reaches a value known as yield strength, \({\displaystyle \sigma _{y}}\). The von Mises stress is used to predict yielding of materials under complex loading from the results of uniaxial tensile tests. The von Mises stress satisfies the property where two stress states with equal distortion energy have an equal von Mises stress.

**Watt**- The SI unit of power, rate of doing work.
**Wave**- Is a disturbance that transfers energy through matter or space, with little or no associated mass transport. Waves consist of oscillations or vibrations of a physical medium or a field, around relatively fixed locations. From the perspective of mathematics, waves, as functions of time and space, are a class of signals.
^{[383]} **Wavelength**- Is the
**spatial period**of a periodic wave—the distance over which the wave's shape repeats.^{[384]}^{[385]}It is thus the inverse of the spatial frequency. Wavelength is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns.^{[386]}^{[387]}Wavelength is commonly designated by the Greek letter*lambda*(λ). The term*wavelength*is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.^{[388]}' . **Wedge**- Is a triangular shaped tool, and is a portable inclined plane, and one of the six classical simple machines. It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by converting a force applied to its blunt end into forces perpendicular (normal) to its inclined surfaces. The mechanical advantage of a wedge is given by the ratio of the length of its slope to its width.
^{[389]}^{[390]}Although a short wedge with a wide angle may do a job faster, it requires more force than a long wedge with a narrow angle. **Weighted arithmetic mean**- The
**weighted arithmetic mean**is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics. If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance in Simpson's paradox. **Wet-bulb temperature**- The temperature of a wetted thermometer with an air current across it. Used in psychrometry. .
**Wheel and axle**- Are one of six simple machines identified by Renaissance scientists drawing from Greek texts on technology.
^{[391]}The wheel and axle consists of a wheel attached to a smaller axle so that these two parts rotate together in which a force is transferred from one to the other. A hinge or bearing supports the axle, allowing rotation. It can amplify force; a small force applied to the periphery of the large wheel can move a larger load attached to the axle. **Winsorized mean**- Is a winsorized statistical measure of central tendency, much like the mean and median, and even more similar to the truncated mean. It involves the calculation of the mean after replacing given parts of a probability distribution or sample at the high and low end with the most extreme remaining values,
^{[392]}typically doing so for an equal amount of both extremes; often 10 to 25 percent of the ends are replaced. The winsorized mean can equivalently be expressed as a weighted average of the truncated mean and the quantiles at which it is limited, which corresponds to replacing parts with the corresponding quantiles. **Work hardening**- Also known as
**strain hardening**, is the strengthening of a metal or polymer by plastic deformation. This strengthening occurs because of dislocation movements and dislocation generation within the crystal structure of the material.^{[393]}

**X-axis**- In algebraic geometry, the axis on a graph that is usually drawn left to right and usually shows the range of values of an independent variable.
^{[394]}

**Y-axis**- In algebraic geometry, the axis on a graph that is usually drawn from bottom to top and usually shows the range of values of variable dependent on one other variable, or the second of two independent variables.
^{[395]} **Yield**- The point of maximum elastic deformation of a material; above yield the material is permanently deformed.
**Young's modulus**- A measure of the stiffness of a material; the amount of force per unit area require to produce a unit strain.

**Z-axis**- In algebraic geometry, the axis on a graph of at least three dimensions that is usually drawn vertically and usually shows the range of values of a variable dependent on two other variables or the third independent variable.
^{[396]} **Zero defects**- A quality assurance philosophy that aims to reduce the need for inspection of components by improving their quality.
**Zero force member**- In the field of engineering mechanics, a
**zero force member**is a member (a single truss segment) in a truss which, given a specific load, is at rest: neither in tension, nor in compression. In a truss a zero force member is often found at pins (any connections within the truss) where no external load is applied and three or fewer truss members meet. Recognizing basic zero force members can be accomplished by analyzing the forces acting on an individual pin in a physical system.*NOTE: If the pin has an external force or moment applied to it, then all of the members attached to that pin are not zero force members UNLESS the external force acts in a manner that fulfills one of the rules below:*- If two non-collinear members meet in an unloaded joint, both are zero-force members.
- If three members meet in an unloaded joint of which two are collinear, then the third member is a zero-force member.

**Reasons for Zero-force members in a truss system**- These members contribute to the stability of the structure, by providing buckling prevention for long slender members under compressive forces
- These members can carry loads in the event that variations are introduced in the normal external loading configuration.

**Zeroth law of thermodynamics**- The equivalence principle applied to temperature; two systems in thermal equiplbirum with a third are also in thermal equilibrium with each other.

- Engineering
- National Council of Examiners for Engineering and Surveying
- Fundamentals of Engineering Examination
- Principles and Practice of Engineering Examination
- Graduate Aptitude Test in Engineering
- Glossary of aerospace engineering
- Glossary of civil engineering
- Glossary of electrical and electronics engineering
- Glossary of mechanical engineering
- Glossary of structural engineering
- Glossary of architecture
- Glossary of areas of mathematics
- Glossary of artificial intelligence
- Glossary of astronomy
- Glossary of biology
- Glossary of calculus
- Glossary of chemistry
- Glossary of ecology
- Glossary of economics
- Glossary of physics
- Glossary of probability and statistics
- List of established military terms#Engineering

**^**The second law of thermodynamics imposes limitations on the capacity of a system to transfer energy by performing work, since some of the system's energy might necessarily be*consumed*in the form of heat instead. See e.g. Lehrman, Robert L. (1973). "Energy Is Not The Ability To Do Work".*The Physics Teacher*.**11**(1): 15–18. Bibcode:1973PhTea..11...15L . doi:10.1119/1.2349846 . ISSN 0031-921X .**^**The words**map**,**mapping**,**transformation**,**correspondence**, and**operator**are often used synonymously. Halmos 1970, p. 30 .

**^**"Newtonian constant of gravitation" is the name introduced for*G*by Boys (1894). Use of the term by T.E. Stern (1928) was misquoted as "Newton's constant of gravitation" in*Pure Science Reviewed for Profound and Unsophisticated Students*(1930), in what is apparently the first use of that term. Use of "Newton's constant" (without specifying "gravitation" or "gravity") is more recent, as "Newton's constant" was also used for the heat transfer coefficient in Newton's law of cooling, but has by now become quite common, e.g. Calmet et al,*Quantum Black Holes*(2013), p. 93; P. de Aquino,*Beyond Standard Model Phenomenology at the LHC*(2013), p. 3.The name "Cavendish gravitational constant", sometimes "Newton–Cavendish gravitational constant", appears to have been common in the 1970s to 1980s, especially in (translations from) Soviet-era Russian literature, e.g. Sagitov (1970 [1969]),*Soviet Physics: Uspekhi*30 (1987), Issues 1–6, p. 342 [etc.]. "Cavendish constant" and "Cavendish gravitational constant" is also used in Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, "Gravitation", (1973), 1126f.Colloquial use of "Big G", as opposed to "little g" for gravitational acceleration dates to the 1960s (R.W. Fairbridge,*The encyclopedia of atmospheric sciences and astrogeology*, 1967, p. 436; note use of "Big G's" vs. "little g's" as early as the 1940s of the Einstein tensor*G*_{μν}vs. the metric tensor*g*_{μν},*Scientific, medical, and technical books published in the United States of America: a selected list of titles in print with annotations: supplement of books published 1945–1948*, Committee on American Scientific and Technical Bibliography National Research Council, 1950, p. 26).**^**Integral calculus is a very well established mathematical discipline for which there are many sources. See Apostol 1967 and Anton, Bivens & Davis 2016 , for example.

**^**For example, the SI unit of velocity is the metre per second, m⋅s^{−1}; of acceleration is the metre per second squared, m⋅s^{−2}; etc.**^**For example the newton (N), the unit of force, equivalent to kg⋅m⋅s^{−2}; the joule (J), the unit of energy, equivalent to kg⋅m^{2}⋅s^{−2}, etc. The most recently named derived unit, the katal, was defined in 1999.**^**For example, the recommended unit for the electric field strength is the volt per metre, V/m, where the volt is the derived unit for electric potential difference. The volt per metre is equal to kg⋅m⋅s^{−3}⋅A^{−1}when expressed in terms of base units.

**^**IUPAC Gold Book - absolute electrode potential**^**"Unit of thermodynamic temperature (kelvin)" .*SI Brochure, 8th edition*. Bureau International des Poids et Mesures. 13 March 2010 [1967]. Section 2.1.1.5. Archived from the original on 7 October 2014. Retrieved 20 June 2017.**Note**: The triple point of water is 0.01 °C, not 0 °C; thus 0 K is −273.15 °C, not −273.16 °C.**^**Arora, C. P. (2001).*Thermodynamics*. Tata McGraw-Hill. Table 2.4 page 43. ISBN 978-0-07-462014-4.**^**Zielinski, Sarah (1 January 2008). "Absolute Zero" . Smithsonian Institution. Retrieved 2012-01-26.**^**IUPAC,*Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Absorbance ". doi:10.1351/goldbook.A00028**^**IUPAC Gold Book - acid**^**Knowles, J. R. (1980). "Enzyme-catalyzed phosphoryl transfer reactions".*Annu. Rev. Biochem*.**49**: 877–919. doi:10.1146/annurev.bi.49.070180.004305 . PMID 6250450 .**^**"Aerobic Diestion" (PDF). Water Environment Federation. Archived from the original (PDF) on 27 March 2016. Retrieved 19 March 2016.**^**"Handbook Biological Wastewater Treatment - Design of Activated Sludge Systems" . Retrieved 19 March 2016.**^***Encyclopedia of Aerospace Engineering*. John Wiley & Sons, 2010. ISBN 978-0-470-75440-5.**^**Daniel Malacara, Zacarias Malacara, Handbook of optical design. Page 379**^**"Alkanes" .*IUPAC Gold Book - alkanes*. IUPAC. March 27, 2017. doi:10.1351/goldbook.A00222 . ISBN 978-0-9678550-9-7. Retrieved 2018-08-23.**^**Wade, L.G. (2006).*Organic Chemistry*(6th ed.). Pearson Prentice Hall. p. 279 . ISBN 978-1-4058-5345-3.**^**Alkyne . Encyclopædia Britannica**^**Callister, W. D. "Materials Science and Engineering: An Introduction" 2007, 7th edition, John Wiley and Sons, Inc. New York, Section 4.3 and Chapter 9.**^**"Amino" .*Dictionary.com*. 2015. Retrieved 3 July 2015.**^**"amino acid" .*Cambridge Dictionaries Online*. Cambridge University Press. 2015. Retrieved 3 July 2015.**^**"amino" .*FreeDictionary.com*. Farlex. 2015. Retrieved 3 July 2015.**^**Wagner I, Musso H (November 1983). "New Naturally Occurring Amino Acids".*Angewandte Chemie International Edition in English*.**22**(11): 816–28. doi:10.1002/anie.198308161 .**^**IUPAC,*Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "amphoteric ". doi:10.1351/goldbook.A00306**^**Knopp, Konrad; Bagemihl, Frederick (1996).*Theory of Functions Parts I and II*. Dover Publications. p. 3. ISBN 978-0-486-69219-7.**^**National Non-Food Crops Centre. "NNFCC Renewable Fuels and Energy Factsheet: Anaerobic Digestion" , Retrieved on 2011-11-22**^**"Angular Velocity and Acceleration" . Theory.uwinnipeg.ca. Archived from the original on 2012-02-22. Retrieved 2015-04-13.**^**University of Colorado Boulder (November 21, 2013). "Atoms and Elements, Isotopes and Ions" . colorado.edu.**^**"Antimatter" . Lawrence Berkeley National Laboratory. Archived from the original on 23 August 2008. Retrieved 3 September 2008.**^**"The Standard Model – Particle decays and annihilations" .*The Particle Adventure: The Fundamentals of Matter and Force*. Lawrence Berkeley National Laboratory. Retrieved 17 October 2011.**^**RFC 4949**^**"ATMAE Venn Diagram" . Archived from the original on 2017-06-30. Retrieved 2018-11-15.**^**"What is buoyant force?" .- ^
^{a}^{b}Acott, Chris (1999). "The diving "Law-ers": A brief resume of their lives" .*South Pacific Underwater Medicine Society Journal*.**29**(1). ISSN 0813-1988 . OCLC 16986801 . Archived from the original on 2011-04-02. Retrieved 2011-06-14.. **^**Jacobs, Harold R. (1994).*Mathematics: A Human Endeavor*(Third ed.). W. H. Freeman. p. 547. ISBN 978-0-7167-2426-1.**^**IUPAC,*Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "arenes ". doi:10.1351/goldbook.A00435**^**Mechanisms of Activation of the Aryl Hydrocarbon Receptor by Maria Backlund, Institute of Environmental Medicine, Karolinska Institutet.**^**Arrhenius, S.A. (1889). "Über die Dissociationswärme und den Einfluß der Temperatur auf den Dissociationsgrad der Elektrolyte" .*Z. Phys. Chem.***4**: 96–116. doi:10.1515/zpch-1889-0408 . S2CID 202553486 .**^**Arrhenius, S.A. (1889). "Über die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Säuren".*ibid.***4**: 226–248.**^**Laidler, K. J. (1987)*Chemical Kinetics*, Third Edition, Harper & Row, p.42**^**Kenneth Connors, Chemical Kinetics, 1990, VCH Publishers*Chemical Kinetics: The Study of Reaction Rates in Solution*at Google Books**^**Poole, Mackworth & Goebel 1998, p. 1 .**^**Russell & Norvig 2003, p. 55.**^**Definition of AI as the study of intelligent agents:- Poole, Mackworth & Goebel (1998) , which provides the version that is used in this article. These authors use the term "computational intelligence" as a synonym for artificial intelligence.
^{[38]} - Russell & Norvig (2003) (who prefer the term "rational agent") and write "The whole-agent view is now widely accepted in the field".
^{[39]} - Nilsson 1998
- Legg & Hutter 2007

- Poole, Mackworth & Goebel (1998) , which provides the version that is used in this article. These authors use the term "computational intelligence" as a synonym for artificial intelligence.
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(help)**^**Kuck, David (1978).*Computers and Computations, Vol 1*. John Wiley & Sons, Inc. p. 12. ISBN 978-0471027164.**^**Bornens, M.; Azimzadeh, J. (2008). "Origin and Evolution of the Centrosome" .*Eukaryotic Membranes and Cytoskeleton*. Advances in Experimental Medicine and Biology.**607**. pp. 119–129 . doi:10.1007/978-0-387-74021-8_10 . ISBN 978-0-387-74020-1. PMID 17977464 .**^**Schmit (2002).*Acentrosomal microtubule nucleation in higher plants*. International Review of Cytology.**220**. pp. 257–289. doi:10.1016/S0074-7696(02)20008-X . ISBN 9780123646248. PMID 12224551 .**^**Jaspersen, S. L.; Winey, M. (2004). "THE BUDDING YEAST SPINDLE POLE BODY: Structure, Duplication, and Function".*Annual Review of Cell and Developmental Biology*.**20**(1): 1–28. doi:10.1146/annurev.cellbio.20.022003.114106 . PMID 15473833 .**^**Fullick, P. (1994),*Physics*, Heinemann, pp. 141–142, ISBN 0-435-57078-1**^**Atkins, Peter; De Paula, Julio (2006).*Atkins' Physical Chemistry*(8th ed.). W. H. Freeman. pp. 200–202 . ISBN 978-0-7167-8759-4.**^**Atkins, Peter W.; Jones, Loretta (2008).*Chemical Principles: The Quest for Insight*(2nd ed.). ISBN 978-0-7167-9903-0.**^**IUPAC,*Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "chemical equilibrium ". doi:10.1351/goldbook.C01023**^**IUPAC,*Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "chemical reaction ". doi:10.1351/goldbook.C01033**^**"What is Chemistry?" . Chemweb.ucc.ie. Retrieved 12 June 2011.**^**"Definition of CHEMISTRY" .*www.merriam-webster.com*. Retrieved 24 August 2020.**^**"Definition of chemistry | Dictionary.com" .*www.dictionary.com*. Retrieved 24 August 2020.**^**"Chemistry Is Everywhere" .*American Chemical Society*.**^**Clausius, R. (1850). "Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen" [On the motive power of heat and the laws which can be deduced therefrom regarding the theory of heat].*Annalen der Physik*(in German).**155**(4): 500–524. Bibcode:1850AnP...155..500C . doi:10.1002/andp.18501550403 . hdl:2027/uc1.$b242250 .**^**Clapeyron, M. C. (1834). "Mémoire sur la puissance motrice de la chaleur" .*Journal de l'École Polytechnique*(in French).**23**: 153–190. ark:/12148/bpt6k4336791/f157.**^****Clausius theorem**at Wolfram Research**^**Finn, Colin B. P.*Thermal Physics*. 2nd ed., CRC Press, 1993.**^**Giancoli, Douglas C.*Physics: Principles with Applications*. 6th ed., Pearson/Prentice Hall, 2005.**^**Mortimer, R. G.*Physical Chemistry*. 3rd ed., p. 120, Academic Press, 2008.**^**"Archived copy" (PDF). Archived from the original (PDF) on 2013-01-24. Retrieved 2013-10-16.CS1 maint: archived copy as title (link)**^**"COP (Coefficient of performance)" .**^**"Archived copy" (PDF). Archived from the original (PDF) on 2009-01-07. Retrieved 2013-10-16.CS1 maint: archived copy as title (link)**^**colloquial meaning of burning is combustion accompanied by flames**^**Narayan, K. Lalit (2008).*Computer Aided Design and Manufacturing*. New Delhi: Prentice Hall of India. p. 3. ISBN 978-8120333420.**^**Narayan, K. Lalit (2008).*Computer Aided Design and Manufacturing*. New Delhi: Prentice Hall of India. p. 4. ISBN 978-8120333420.**^**Duggal, Vijay (2000).*Cadd Primer: A General Guide to Computer Aided Design and Drafting-Cadd, CAD*. Mailmax Pub. ISBN 978-0962916595.- ^
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^{a}^{b}"The Inclined Plane" .*Math and science activity center*. Edinformatics. 1999. Retrieved March 11, 2012. **^**https://en.wiktionary.org/wiki/indefinite_integral Wiktionary**^**Serway, A. Raymond; Jewett, John W.; Wilson, Jane; Wilson, Anna; Rowlands, Wayne (1 October 2016). "32".*Physics for global scientists and engineers*(2ndition ed.). p. 901. ISBN 9780170355520.**^**Alexander, Charles; Sadiku, Matthew.*Fundamentals of Electric Circuits*(3 ed.). McGraw-Hill. p. 211.**^**Salvendy, Gabriel. Handbook of Industrial Engineering. John Wiley & Sons, Inc; 3rd edition p. 5**^**"What IEs Do" .*www.iienet2.org*. Retrieved September 24, 2015.**^**"Careers in Chemistry: Inorganic Chemistry" . American Chemical Society. Archived from the original on 2012-10-29.**^**"Ionic bond" .*IUPAC Compendium of Chemical Terminology*. 2009. doi:10.1351/goldbook.IT07058 . ISBN 978-0-9678550-9-7.**^**Herzog, Gregory F. (2 June 2020). "Isotope" . Encyclopedia Britannica.**^**International Bureau of Weights and Measures (2006),*The International System of Units (SI)*(PDF) (8th ed.), p. 120, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14**^**American Heritage Dictionary of the English Language , Online Edition (2009). Houghton Mifflin Co., hosted by Yahoo! Education .**^***The American Heritage Dictionary*, Second College Edition (1985). Boston: Houghton Mifflin Co., p. 691.**^***McGraw-Hill Dictionary of Physics*, Fifth Edition (1997). McGraw-Hill, Inc., p. 224.**^**Rao, Y. V. C. (1997).*Chemical Engineering Thermodynamics*. Universities Press. p. 158. ISBN 978-81-7371-048-3.**^**Young, Hugh D.; Freedman, Roger A. (2008).*University Physics*.**1**(12 ed.). Pearson Education. ISBN 978-0-321-50125-7.**^**Edmund Taylor Whittaker (1904).*A Treatise on the Analytical Dynamics of Particles and Rigid Bodies*. Cambridge University Press. Chapter 1. ISBN 0-521-35883-3.**^**Joseph Stiles Beggs (1983).*Kinematics*. Taylor & Francis. p. 1. ISBN 0-89116-355-7.**^**Thomas Wallace Wright (1896).*Elements of Mechanics Including Kinematics, Kinetics and Statics*. E and FN Spon. Chapter 1.**^**Streeter, V.L. (1951-1966)*Fluid Mechanics*, Section 3.3 (4th edition). McGraw-Hill**^**Geankoplis, Christie John (2003).*Transport Processes and Separation Process Principles*. Prentice Hall Professional Technical Reference. ISBN 978-0-13-101367-4. Archived from the original on 2015-05-01.**^**Noakes, Cath; Sleigh, Andrew (January 2009). "Real Fluids" .*An Introduction to Fluid Mechanics*. University of Leeds. Archived from the original on 21 October 2010. Retrieved 23 November 2010.**^**"Laplace Transform: A First Introduction" .*Math Vault*. Retrieved 2020-08-08.**^**"Differential Equations - Laplace Transforms" .*tutorial.math.lamar.edu*. Retrieved 2020-08-08.**^**Weisstein, Eric W. "Laplace Transform" .*mathworld.wolfram.com*. Retrieved 2020-08-08.- ^
^{a}^{b}Gall, John (2002).*The Systems Bible*(3rd ed.). General Systemantics Press.The System always kicks back

**^**Lenz, E. (1834), "Ueber die Bestimmung der Richtung der durch elektodynamische Vertheilung erregten galvanischen Ströme ",*Annalen der Physik und Chemie*,**107**(31), pp. 483–494. A partial translation of the paper is available in Magie, W. M. (1963),*A Source Book in Physics*, Harvard: Cambridge MA, pp. 511–513.**^**Schmitt, Ron.*Electromagnetics explained*. 2002. Retrieved 16 July 2010.**^**"Lepton (physics)" .*Encyclopædia Britannica*. Retrieved 2010-09-29.**^**CIE (1987).*International Lighting Vocabulary*Archived 27 February 2010 at the Wayback Machine. Number 17.4. CIE, 4th edition. ISBN 978-3-900734-07-7.

By the*International Lighting Vocabulary*, the definition of*light*is: "Any radiation capable of causing a visual sensation directly."**^**Pal, G.K.; Pal, Pravati (2001). "chapter 52" .*Textbook of Practical Physiology*(1st ed.). Chennai: Orient Blackswan. p. 387. ISBN 978-81-250-2021-9. Retrieved 11 October 2013.The human eye has the ability to respond to all the wavelengths of light from 400–700 nm. This is called the visible part of the spectrum.

**^**Buser, Pierre A.; Imbert, Michel (1992).*Vision*. MIT Press. p. 50 . ISBN 978-0-262-02336-8. Retrieved 11 October 2013.Light is a special class of radiant energy embracing wavelengths between 400 and 700 nm (or mμ), or 4000 to 7000 Å.

**^**"The Ultimate Guide to Logarithm — Theory & Applications" ,*Math Vault*, 8 May 2016, retrieved 24 July 2019**^**All statements in this section can be found in Shirali 2002, Section 4 , Downing 2003, p. 275 , or Kate & Bhapkar 2009, p. 1-1 , for example.**^**Incropera; DeWitt; Bergman; Lavine (2007).*Fundamentals of Heat and Mass Transfer*(6th ed.). John Wiley & Sons. pp. 260 –261. ISBN 978-0-471-45728-2.**^**John, Blyler (27 December 2019). "What is middle-out systems engineering?" .*DesignNews*. Retrieved 28 September 2020.**^**Close, Frank (2010). Neutrinos (softcover ed.). Oxford University Press. ISBN 978-0-199-69599-7.- ^
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