NationMaster - Encyclopedia: List of equations

This is a list of equations, by Wikipedia page. See also list of equations in classical mechanics, list of relativistic equations, equation solving, theory of equations. In mathematics, one often (not quite always) distinguishes between an identity, which is an assertion that two expressions are equal regardless of the values of any variables that occur within them, and an equation, which may be true for only some (or none) of the values of any such variables. ... This page gives a summary of important equations in classical mechanics. ... // Special relativistic equations Special Relativity was put forth by Albert Einstein and is possibly his most famous contribution to science. ... In mathematics, equation solving is the problem of finding what values (numbers, functions, sets, etc. ... In mathematics, the theory of equations comprises a major part of traditional algebra. ...

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The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of a chemical reaction rate. ... In fluid dynamics, Bernoullis equation, derived by Daniel Bernoulli, describes the behavior of a fluid moving along a streamline. ... The Black-Scholes model, often simply called Black-Scholes, is a model of the varying price over time of financial instruments, and in particular stocks. ... In mathematics, the Cauchy-Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, are two partial differential equations which provide a necessary and sufficient condition for a function to be holomorphic. ... In mathematics, specifically in probability theory, and yet more specifically in the theory of stochastic processes, the Chapman-Kolmogorov equation is an identity relating the joint probability distributions of different sets of coordinates on a stochastic process. ... In mathematics, a Clairauts equation is a differential equation of the form To solve such an equation, we differentiate with respect to x, yielding so Hence, either or In the former case, C = dy/dx for some constant C. Substituting this into the Clairauts equation, we have the... The Darcy-Weisbach equation is an important and widely used equation in hydraulics. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by Paul Dirac in 1928 and provides a description of elementary spin-Â½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ... The Drake equation (also known as the Green Bank equation or the Sagan equation) is a famous result in the speculative fields of xenobiology, astrosociobiology and the search for extraterrestrial intelligence. ... In physics, the Einstein field equation or Einstein equation is a differential equation in Einsteins theory of general relativity. ... In fluid dynamics, the Euler equations govern the motion of a compressible, inviscid fluid. ... In fluid mechanics and astrophysics, the relativistic Euler equations are a generalization of the Euler equations that account for the effects of special relativity. ... The Euler-Lagrange Equation is the major formula of the Calculus of variations. ... In physics, the action principle is an assertion about the nature of motion from which the trajectory of an object subject to forces can be determined. ... NOTE: this is not Fishers equation in differential equations The Fisher equation in financial mathematics and economics estimates the relationship between nominal and real interest rates under inflation. ... The Fokker-Planck equation (named after Adriaan Fokker and Max Planck; also known as the Kolmogorov Forward equation) describes the time evolution of the probability density function of position and velocity of a particle. ... In mathematics, the Fredholm integral equation introduced by Ivar Fredholm gives rises to a Fredholm operator. ... The Fresnel equations, deduced by Augustin-Jean Fresnel, describe the behaviour of light when moving between media of differing refractive indices. ... The Friedmann equations relate various cosmological parameters within the context of general relativity. ... The Gibbs-Helmholtz equation is a thermodynamic relationship useful for calculating changes in the energy or enthalpy (heat content) of a system. ... The Drake equation (also known as the Green Bank equation) is a famous result in the speculative fields of xenobiology, astrosociobiology and the search for extraterrestrial intelligence. ... The Hamilton-Jacobi-Bellman (HJB) equation is a partial differential equation which is central to optimal control theory. ... The Henderson-Hasselbalch equation in chemistry describes the derivation of pH as a measure of acidity (using pKa, the acid dissociation constant) in biological and chemical systems. ... To compute the position of a satellite at a given time using Keplers laws of planetary motion (the Keplerian problem) is a difficult problem. ... The Klein-Gordon equation (Klein-Fock-Gordon equation or sometimes Klein-Gordon-Fock equation) is the relativistic version of the SchrÃ¶dinger equation. ... The Korteweg-de Vries equation (KdV equation for short) is the following partial differential equation for a function φ of two real variables, x and t: Its solutions clump up into solitons. ... In astrophysics, the Lane-Emden equation is applicable to magnetohydrodynamic fluids under the action of force-free magnetic fields. ... In statistical physics, a Langevin equation is a stochastic differential equation describing Brownian motion in a potential. ... In mathematics, Laplaces equation is a partial differential equation named after its discoverer Pierre-Simon Laplace. ... The Lindblad equation or master equation in the Lindblad form is the most general type of master equation allowed by Quantum mechanics to describe non-unitary (dissipative) evolution of the density matrix (such as ensuring normalisation and hermiticity of ). It reads: where is the density matrix, is the hamiltonian part... The electromagnetic field (EMF) is composed of two related vectorial fields, the electric field and the magnetic field. ... In mathematics, the Maurer-Cartan form for a Lie group G is a distinguished differential form on G that carries within itself the basic infinitesimal information about the structure of G. It was much used by Elie Cartan, as a basic ingredient of his method of moving frames. ... Maxwells equations (sometimes called the Maxwell equations) are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... Michaelis-Menten kinetics describe the rate of enzyme mediated reactions for many enzymes. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances like liquids and gases. ... The Reynolds-averaged Navier-Stokes equations are time-averaged equations of motion for fluid flow. ... In electrochemistry, the Nernst equation gives the electrode potential (E), relative to the standard electrode potential, (E0), of the electrode couple or, equivalently, of the half cells of a battery. ... Pells equation is any Diophantine equation of the form where n is a nonsquare integer. ... In mathematics, Poissons equation is a partial differential equation with broad utility in electrostatics, mechanical engineering and theoretical physics. ... The Prony equation is a historically important equation in hydraulics, used to calculate the head loss due to friction within a given run of pipe. ... The Rankine-Hugoniot equation governs the behaviour of shock waves. ... In mathematics, a Riccati equation is any ordinary differential equation that has the form It is named after Count Jacopo Francesco Riccati (1676-1754). ... The Roothaan equations are a representation of the Hartree-Fock equation in a non orthonormalized basis set which can be of Gaussian type. ... In physics, the SchrÃ¶dinger equation, proposed by the Austrian physicist Erwin SchrÃ¶dinger in 1925, describes the time-dependence of quantum mechanical systems. ... The screened Poisson equation is the following partial differential equation: where ² is the Laplace operator, λ is a constant, and f is an arbitrary function of position (known as the source function.) The screened Poisson equation occurs frequently in physics, including Yukawas theory of mesons and electric field... The Schwinger-Dyson equation, named after Julian Schwinger and Freeman Dyson, is an equation of quantum field theory (QFT). ... A plot of the refractive index vs. ... The Sine-Gordon equation is a partial differential equation for a function of two real variables, x and t, given as follows: The name is a pun on the Klein-Gordon equation. ... Tsiolkovskys rocket equation, named after Konstantin Tsiolkovsky who independently derived it, considers the principle of a rocket: a device that can apply an acceleration to itself (a thrust) by expelling part of its mass with high speed in the opposite direction, due to the conservation of momentum. ... The van der Waals equation is an equation of state for a fluid composed of particles that have a non-zero size and a pairwise attractive inter-particle force (such as the van der Waals force. ... The logistic function or logistic curve is defined by the mathematical formula: for real parameters a, m, n, and . ... The Lotka-Volterra equations, also known as the predator-prey equations, are a pair of first order, non-linear, differential equations frequently used to describe the dynamics of biological systems in which two species interact, one a predator and one its prey. ... ). A simple mathematical representation of Brownian motion, the Wiener equation, named after Norbert Wiener, assumes the current velocity of a fluid particle fluctuates randomly: where v is velocity, x is position, d/dt is the time derivative, and g(t) may for instance be white noise. ...

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Categories: Equations | Differential equations | Mathematical lists The advection equation is the partial differential equation that governs the motion of a conserved scalar as it is advected by a known velocity field. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... A linear equation is an equation involving only the sum of constants or products of constants and the first power of a variable. ... Graph of a quadratic function: y = x2 - x - 2 = (x+1)(x-2) The x-coordinates of the points where the graph crosses the x-axis, x = -1 and x = 2, are the roots of the quadratic equation: x2 - x - 2 = 0 In mathematics, a quadratic equation is a polynomial... Graph of a cubic polynomial: y = x3/4 + 3x2/4 âˆ’ 3x/2 âˆ’ 2 = (1/4)(x + 4)(x + 1)(x âˆ’ 2) In mathematics, a cubic equation is a polynomial equation in which the highest occurring power of the unknown is the third power. ... In mathematics, a quartic equation is the result of setting a quartic function equal to zero. ... In mathematics, a quartic equation is the result of setting a quartic function equal to zero. ... In mathematics, a quintic equation is a polynomial equation in which the greatest exponent on the independent variable is five. ... A simplified form of the vorticity equation for an inviscid, divergence-free flow, the barotropic vorticity equation can simply be stated as where is the material derivative and is absolute vorticity, with being relative vorticity, defined as the vertical component of the curl of the fluid velocity and f is... In linear algebra, the characteristic equation of a square matrix A is the equation in one variable λ where I is the identity matrix. ... A chemical equation is a symbolic representation of a chemical reaction. ... In mathematics, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes reveals many important features of a groups structure. ... A comparametric equation is an equation that describes a parametric relationship between a function and a dilated version of the same function, where the equation does not involve the parameter. ... All the examples of continuity equations below express the same idea; they are all really examples of the same concept. ... In mathematics, a recurrence relation, also known as a difference equation, is an equation which defines a sequence recursively: each term of the sequence is defined as a function of the preceding terms. ... In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... In mathematics, a partial differential equation (PDE) is an equation relating the partial derivatives of an unknown function of several variables. ... In mathematics, a total derivative may mean either (i) a differential operator involving the sum of all the partial derivatives with respect to all variables in a problem, or be used compatibly (ii) to express the exterior derivative d, as applied to differential forms, and in particular as applied to... In mathematics, a Diophantine equation is a polynomial equation that only allows the variables to be integers. ... In physics, the drag equation gives the drag experienced by an object moving through a fluid. ... The theoretical physics equation E = mc2 states a relationship between energy (E), in whatever form, and mass (m). ... In mathematics, one often (not quite always) distinguishes between an identity, which is an assertion that two expressions are equal regardless of the values of any variables that occur within them, and an equation, which may be true for only some (or none) of the values of any such variables. ... In elementary physics and linear kinematics, the equations of motion are five equations that apply to bodies moving linearly (that is, one dimension) with uniform acceleration. ... In physics and thermodynamics, an equation of state is a constitutive equation describing the state of matter under a given set of physical conditions. ... A molecular equation is a chemical equation written as if all components exist as molecules. ... The heat equation is an important partial differential equation which describes the variation of temperature in a given region over time. ... An ionic equation is a chemical equation in which strong electrolytes are written as dissociated ions. ... In mathematics, a modular equation is an algebraic equation satisfied by moduli, in the sense of moduli problem. ... A molecular equation is a chemical equation written as if all components exist as molecules. ... Graph of a butterfly curve, a parametric equation discovered by Temple H. Fay In mathematics, a parametric equation explicitly relates two or more variables in terms of one or more independent parameters. ... In telecommunication, a password length equation is an equation that determines an appropriate password length, M , which provides an acceptable probability, P , that a password will be guessed in its lifetime. ... The primitive equations are a version of the Navier-Stokes equations which describe hydrodynamical flow on the sphere under the assumptions that vertical motion is much smaller than horizontal motion (hydrostasis) and that the fluid layer depth is small compared to the radius of the sphere. ... Before the creation of quantum field theory, physicists attempted to formulate versions of the Schrödinger equation which were compatible with special relativity. ... The replicator equation is a differential equation that defines the dynamics of evolutionary games. ... Oliver Heaviside developed the transmission line theory known as the telegraphers equations. ... A Thermochemical Equation is a balanced stoichiometric chemical equation that includes the enthalpy change, Î”H. In variable form, a thermochemical equation would look like this: A + B â†’ C Î”H = (Â±) # Where {A, B, C} are the usual agents of a chemical equation with coefficients and â€œ(Â±) #â€ is a positive or negative numerical... The ideal gas law, or universal gas equation, is an equation of state of an ideal gas. ... The vorticity equation is an important prognostic equation in the atmospheric sciences. ... The wave equation is an important partial differential equation which generally describes all kinds of waves, such as sound waves, light waves and water waves. ...

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