This is a list of

equation In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in ...

s, by Wikipedia page under appropriate bands of maths, science and engineering.

Eponymous equations

Mathematics

Cauchy–Riemann equations In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which, together with certain continuity and differenti ...

* Chapman–Kolmogorov equation * Maurer–Cartan equation *

Pell's equation Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form x^2 - ny^2 = 1, where ''n'' is a given positive nonsquare integer, and integer solutions are sought for ''x'' and ''y''. In Cartesian coordinates, ...

Poisson's equation Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with t ...

Riccati equation In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function. In other words, it is an equation of the form : y'(x) = q_0(x) + q_1(x) \, y(x) + q_2(x) \, y^2( ...

* sine-Gordon equation *

Verhulst equation A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation f(x) = \frac, where For values of x in the domain of real numbers from -\infty to +\infty, the S-curve shown on the right is obtained, with the ...

Physics

* Ampère's circuital law *

Bernoulli's equation In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after the Swiss mathematic ...

* Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy of equations *

Bessel's differential equation Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary ...

Boltzmann equation The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lerne ...

* Borda–Carnot equation *

Burgers' equation Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas of applied mathematics, such as fluid mechanics, nonlinear acoustics, gas dynamics, and tr ...

Darcy–Weisbach equation In fluid dynamics, the Darcy–Weisbach equation is an empirical equation that relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. The equation ...

Dirac equation In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles, called "Dirac par ...

Dirac equation in the algebra of physical space In physics, the algebra of physical space (APS) is the use of the Clifford algebra, Clifford or geometric algebra Cl3,0(R) of the three-dimensional Euclidean space as a model for (3+1)-dimensional spacetime, representing a point in spacetime via a ...

* Dirac–Kähler equation * Doppler equations *

Drake equation The Drake equation is a probabilistic argument used to estimate the number of active, communicative extraterrestrial civilizations in the Milky Way Galaxy. The equation was formulated in 1961 by Frank Drake, not for purposes of quantifying ...

(aka Green Bank equation) *

Einstein's field equations In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form ...

Euler equations (fluid dynamics) In fluid dynamics, the Euler equations are a set of quasilinear partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations wit ...

Euler's equations (rigid body dynamics) In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to th ...

Relativistic Euler equations In fluid mechanics and astrophysics, the relativistic Euler equations are a generalization of the Euler equations that account for the effects of general relativity. They have applications in high-energy astrophysics and numerical relativity, whe ...

Euler–Lagrange equation In the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered ...

* Faraday's law of induction * Fokker–Planck equation *

Fresnel equations The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media. They were deduced by Augustin-Jean Fres ...

Friedmann equations The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann ...

* Gauss's law for electricity *

Gauss's law for gravity In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is equivalent to Newton's law of universal gravitation. It is named after Carl Friedrich Gauss. It states that the flux ( surface integ ...

Gauss's law for magnetism In physics, Gauss's law for magnetism is one of the four Maxwell's equations that underlie classical electrodynamics. It states that the magnetic field has divergence equal to zero, in other words, that it is a solenoidal vector field. It is ...

Gibbs–Helmholtz equation The Gibbs–Helmholtz equation is a thermodynamic equation used for calculating changes in the Gibbs free energy of a system as a function of temperature. It was originally presented in an 1882 paper entitled " Die Thermodynamik chemischer Vorgang ...

Gross–Pitaevskii equation The Gross–Pitaevskii equation (GPE, named after Eugene P. Gross and Lev Petrovich Pitaevskii) describes the ground state of a quantum system of identical bosons using the Hartree–Fock approximation and the pseudopotential interaction model. ...

Hamilton–Jacobi–Bellman equation In optimal control theory, the Hamilton-Jacobi-Bellman (HJB) equation gives a necessary and sufficient condition for optimality of a control with respect to a loss function. It is, in general, a nonlinear partial differential equation in the value ...

* Helmholtz equation *

Karplus equation The Karplus equation, named after Martin Karplus, describes the correlation between 3J-coupling constants and dihedral torsion angles in nuclear magnetic resonance spectroscopy: :J(\phi) = A \cos^2 \phi + B \cos\,\phi + C where ''J'' is the 3''J ...

Kepler's equation In orbital mechanics, Kepler's equation relates various geometric properties of the orbit of a body subject to a central force. It was first derived by Johannes Kepler in 1609 in Chapter 60 of his ''Astronomia nova'', and in book V of his '' Epi ...

* Kepler's laws of planetary motion *

Kirchhoff's diffraction formula Kirchhoff's diffraction formula (also Fresnel–Kirchhoff diffraction formula) can be used to model the propagation of light in a wide range of configurations, either analytically or using numerical modelling. It gives an expression for the wave d ...

Klein–Gordon equation The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. It is second-order in space and time and manifestly Lorentz-covariant ...

* Korteweg–de Vries equation *

Landau–Lifshitz–Gilbert equation In physics, the Landau–Lifshitz–Gilbert equation, named for Lev Landau, Evgeny Lifshitz, and T. L. Gilbert, is a name used for a differential equation describing the precessional motion of magnetization in a solid. It is a modification by Gi ...

* Lane–Emden equation * Langevin equation * Levy–Mises equations *

Lindblad equation In quantum mechanics, the Gorini–Kossakowski–Sudarshan–Lindblad equation (GKSL equation, named after Vittorio Gorini, Andrzej Kossakowski, George Sudarshan and Göran Lindblad), master equation in Lindblad form, quantum Liouvillian, or Li ...

* Lorentz equation *

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...

* Maxwell's relations *

Newton's laws of motion Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in moti ...

Navier–Stokes equations In physics, the Navier–Stokes equations ( ) are 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 Geo ...

Reynolds-averaged Navier–Stokes equations The Reynolds-averaged Navier–Stokes equations (RANS equations) are time-averaged equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition, whereby an instantaneous quantity is decomposed into its time-averaged ...

* Prandtl–Reuss equations *

Prony equation The Prony equation (named after Gaspard de Prony) is a historically important equation in hydraulics, used to calculate the head loss due to friction within a given run of pipe. It is an empirical equation developed by Frenchman Gaspard de Prony ...

* Rankine–Hugoniot equation *

Roothaan equations The Roothaan equations are a representation of the Hartree–Fock equation in a non orthonormal basis set which can be of Gaussian-type or Slater-type. It applies to closed-shell molecules or atoms where all molecular orbitals or atomic orbitals ...

Saha ionization equation In physics, the Saha ionization equation is an expression that relates the ionization state of a gas in thermal equilibrium to the temperature and pressure. The equation is a result of combining ideas of quantum mechanics and statistical mechanics ...

Sackur–Tetrode equation The Sackur–Tetrode equation is an expression for the entropy of a monatomic ideal gas. It is named for Hugo Martin Tetrode (1895–1931) and Otto Sackur (1880–1914), who developed it independently as a solution of Boltzmann's gas statistics an ...

* Samik Hazra equation *

Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...

screened Poisson equation In physics, the screened Poisson equation is a Poisson equation, which arises in (for example) the Klein–Gordon equation, electric field screening in plasmas, and nonlocal granular fluidity in granular flow. Statement of the equation The equat ...

Schwinger–Dyson equation The Schwinger–Dyson equations (SDEs) or Dyson–Schwinger equations, named after Julian Schwinger and Freeman Dyson, are general relations between correlation functions in quantum field theories (QFTs). They are also referred to as the Euler� ...

* Sellmeier equation * Stokes–Einstein relation *

Tsiolkovsky rocket equation Konstantin Eduardovich Tsiolkovsky (russian: Константи́н Эдуа́рдович Циолко́вский , , p=kənstɐnʲˈtʲin ɪdʊˈardəvʲɪtɕ tsɨɐlˈkofskʲɪj , a=Ru-Konstantin Tsiolkovsky.oga; – 19 September 1935) ...

Van der Waals equation In chemistry and thermodynamics, the Van der Waals equation (or Van der Waals equation of state) is an equation of state which extends the ideal gas law to include the effects of interaction between molecules of a gas, as well as accounting for ...

Vlasov equation The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range interaction, e.g. Coulomb. The equation was first suggested for description of plasma ...

Wiener equation A simple mathematical representation of Brownian motion, the Wiener equation, named after Norbert Wiener, assumes the current velocity of a fluid particle fluctuates randomly: :\mathbf = \frac = g(t), where v is velocity, x is position, ''d/dt'' ...

Chemistry

Arrhenius equation In physical chemistry, 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 1 ...

* Butler–Volmer equation *

Eyring equation The Eyring equation (occasionally also known as Eyring–Polanyi equation) is an equation used in chemical kinetics to describe changes in the rate of a chemical reaction against temperature. It was developed almost simultaneously in 1935 by Henr ...

Henderson–Hasselbalch equation In chemistry and biochemistry, the Henderson–Hasselbalch equation :\ce = \ceK_\ce + \log_ \left( \frac \right) relates the pH of a chemical solution of a weak acid to the numerical value of the acid dissociation constant, ''K''a, of acid and th ...

* Michaelis–Menten equation *

Nernst equation In electrochemistry, the Nernst equation is a chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction ( half-cell or full cell reaction) from the standard electrode potential, absolute tempe ...

Urey-Bigeleisen-Mayer equation In stable isotope geochemistry, the Urey-Bigeleisen-Mayer equation, also known as the Bigeleisen-Mayer equation or the Urey model, is a model describing the approximate equilibrium isotope fractionation in an isotope exchange reaction. While the e ...

Biology

* Breeder's equation *

Hardy–Weinberg principle In population genetics, the Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or law, states that allele and genotype frequencies in a population will remain constant from generation to generation in t ...

* Hill equation * Lotka–Volterra equation * Michaelis–Menten equation *

Poiseuille equation The poiseuille (symbol Pl) has been proposed as a derived SI unit of dynamic viscosity, named after the French physicist Jean Léonard Marie Poiseuille (1797–1869). In practice the unit has never been widely accepted and most international ...

Price equation In the theory of evolution and natural selection, the Price equation (also known as Price's equation or Price's theorem) describes how a trait or allele changes in frequency over time. The equation uses a covariance between a trait and fitness, ...

Economics

* Black–Scholes equation * Fisher equation

Technology

* Mansour's equation

Other equations

Mathematics

Polynomial equation In mathematics, an algebraic equation or polynomial equation is an equation of the form :P = 0 where ''P'' is a polynomial with coefficients in some field, often the field of the rational numbers. For many authors, the term ''algebraic equation' ...

** Linear equation **

Quadratic equation In algebra, a quadratic equation () is any equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where represents an unknown (mathematics), unknown value, and , , and represent known numbers, where . (If and then the equati ...

Cubic equation In algebra, a cubic equation in one variable is an equation of the form :ax^3+bx^2+cx+d=0 in which is nonzero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of th ...

** Biquadratic equation **

Quartic equation In mathematics, a quartic equation is one which can be expressed as a ''quartic function'' equaling zero. The general form of a quartic equation is :ax^4+bx^3+cx^2+dx+e=0 \, where ''a'' ≠ 0. The quartic is the highest order polynomi ...

Quintic equation In algebra, a quintic function is a function of the form :g(x)=ax^5+bx^4+cx^3+dx^2+ex+f,\, where , , , , and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero. In other words, a ...

Sextic equation In algebra, a sextic (or hexic) polynomial is a polynomial of degree six. A sextic equation is a polynomial equation of degree six—that is, an equation whose left hand side is a sextic polynomial and whose right hand side is zero. More precis ...

* Characteristic equation *

Class equation In mathematics, especially group theory, two elements a and b of a group are conjugate if there is an element g in the group such that b = gag^. This is an equivalence relation whose equivalence classes are called conjugacy classes. In other ...

* Comparametric equation * Difference equation **

Matrix difference equation A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. The order of the eq ...

Differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

Matrix differential equation A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. A matrix differential equation contains more than one funct ...

Ordinary differential equation In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast w ...

Partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

** Total differential equation * Diophantine equation *

Equation In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in ...

* Modular equation * Parametric equation *

Replicator equation In mathematics, the replicator equation is a deterministic monotone non-linear and non-innovative game dynamic used in evolutionary game theory. The replicator equation differs from other equations used to model replication, such as the quasispecie ...

Physics

Advection equation In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is al ...

Barotropic vorticity equation The barotropic vorticity equation assumes the atmosphere is nearly barotropic, which means that the direction and speed of the geostrophic wind are independent of height. In other words, there is no vertical wind shear of the geostrophic wind. I ...

Continuity equation A continuity equation or transport equation 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. S ...

* Diffusion equation *

Drag equation In fluid dynamics, the drag equation is a formula used to calculate the force of drag experienced by an object due to movement through a fully enclosing fluid. The equation is: F_\, =\, \tfrac12\, \rho\, u^2\, c_\, A where *F_ is the drag fo ...

Equation of motion In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Ver ...

Equation of state In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or intern ...

Equation of time In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in F ...

Heat equation In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions. The theory of the heat equation was first developed by Joseph Fourier in 1822 for t ...

Ideal gas equation The 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 sta ...

* Ideal MHD equations * Mass–energy equivalence equation *

Primitive equations The primitive equations are a set of nonlinear partial differential equations that are used to approximate global atmospheric flow and are used in most atmospheric models. They consist of three main sets of balance equations: # A '' continuity e ...

Relativistic wave equations In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light. In the con ...

Vis-viva equation In astrodynamics, the ''vis-viva'' equation, also referred to as orbital-energy-invariance law, is one of the equations that model the motion of orbiting bodies. It is the direct result of the principle of conservation of mechanical energy which ...

* Vorticity equation *

Wave equation The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and s ...

Chemistry

Chemical equation A chemical equation is the symbolic representation of a chemical reaction in the form of symbols and chemical formulas. The reactant entities are given on the left-hand side and the product entities on the right-hand side with a plus sign between ...

(aka molecular equation) * Thermochemical equation

Telecommunications engineering

* Password length equation *

Telegrapher's equations The telegrapher's equations (or just telegraph equations) are a pair of coupled, linear partial differential equations that describe the voltage and current on an electrical transmission line with distance and time. The equations come from Oliver ...

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Lists of equations

Constitutive equation In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approx ...

* Laws of science *

Defining equation (physical chemistry) In physical chemistry, there are numerous quantities associated with chemical compounds and reactions; notably in terms of ''amounts'' of substance, ''activity'' or ''concentration'' of a substance, and the ''rate'' of reaction. This article use ...

Defining equation (physics) In physics, defining equations are equations that define new quantities in terms of base quantities. This article uses the current SI system of units, not natural or characteristic units. Description of units and physical quantities Physical q ...

List of equations in classical mechanics Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. The sub ...

Table of thermodynamic equations This article is a summary of common equations and quantities in thermodynamics (see thermodynamic equations for more elaboration). Definitions Many of the definitions below are also used in the thermodynamics of chemical reactions. General ...

List of equations in wave theory This article summarizes equations in the theory of waves. Definitions General fundamental quantities A wave can be longitudinal where the oscillations are parallel (or antiparallel) to the propagation direction, or transverse where the oscill ...

* List of electromagnetism equations *

List of relativistic equations Following is a list of the frequently occurring equations in the theory of special relativity. Postulates of Special Relativity To derive the equations of special relativity, one must start with two other #The laws of physics are invariant ...

List of equations in fluid mechanics This article summarizes equations in the theory of fluid mechanics. Definitions Here \mathbf \,\! is a unit vector in the direction of the flow/current/flux. Equations See also * Defining equation (physical chemistry) *List of electro ...

List of equations in gravitation This article summarizes equations in the theory of gravitation. Definitions Gravitational mass and inertia A common misconception occurs between centre of mass and centre of gravity. They are defined in similar ways but are not exactly the ...

* List of photonics equations *

List of equations in quantum mechanics This article summarizes equations in the theory of quantum mechanics. Wavefunctions A fundamental physical constant occurring in quantum mechanics is the Planck constant, ''h''. A common abbreviation is , also known as the ''reduced Planck cons ...

List of equations in nuclear and particle physics This article summarizes equations in the theory of nuclear physics and particle physics. Definitions Equations Nuclear structure Nuclear decay Nuclear scattering theory The following apply for the nuclear reaction: :''a'' + ''b'' � ...