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Wikipedia on Equations

:''This article is about equations in mathematics. For the chemistry term, see chemical equation.'' An equation is a mathematical statement, in symbols, that two things are the same . Equations are written with an equal sign, as in :2 + 3 More »
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Differential equation
thumb A differential equation is a mathematical equation for an unknown function of one or several variables which relates the values of the function itself and of its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics, and other disciplines. Differential equations arise in many areas of science and technology, whenever a deterministic relationship involving some continuously changing quantities and their rates of change is known... More »
Integral equation
In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way. See, for example, Maxwell's equations. More »
Diophantine equation
In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. In more technical language, they define an algebraic curve, algebraic surface or more general object, and ask about the lattice points on it. The word ''Diophantine'' refers to the Hellenistic mathematician of the 3rd century CE,... More »
Navier-Stokes equations
The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. These equations establish that changes in momentum in infinitesimal volumes of fluid are simply the sum of dissipative viscous forces , changes in pressure, gravity, and other forces acting inside the fluid: an application of Newton's second law. They are one of the most useful sets of equations because they... More »
Continuity equation
All the examples of continuity equations below express the same idea. Continuity equations are the local form of conservation laws. More »
Minkowski space
In physics and mathematics, Minkowski space is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated. In this setting the three ordinary dimensions of space are combined with a single dimension of time to form a four-dimensional manifold for representing a spacetime. Minkowski space is named for the German mathematician Hermann Minkowski . More »
Fredholm integral equation
In mathematics, the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators. The integral equation was studied by Ivar Fredholm. More »
Exact solutions in general relativity
In general relativity, an exact solution is a Lorentzian manifold equipped with certain tensor fields which are taken to model states of ordinary matter, such as a fluid, or classical nongravitational fields such as the electromagnetic field. These tensor fields should obey any relevant physical laws . Following a standard recipe which is widely used in mathematical physics, these tensor fields should also give rise to specific contributions to the stress-energy tensor... More »
Schwarzschild metric
In Einstein's theory of general relativity, the Schwarzschild solution describes the gravitational field outside a spherical, non-rotating mass such as a star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or Sun. According to Birkhoff's theorem, the Schwarzschild solution is the most general stationary, spherically symmetric, vacuum solution of the Einstein field equations. More »
Vacuum solution (general relativity)
In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress-energy tensor also vanishes identically, so that no matter or non-gravitational fields are present. More generally, a vacuum region in a Lorentzian manifold is a region in which the Einstein tensor vanishes. More »
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