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Calculus. In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may integrate over this surface a scalar field (that is, a function of position which returns a ...
In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in (the real-number plane) are called double integrals, and integrals of a function of three variables over a region ...
Lebedev quadrature. In numerical analysis, Lebedev quadrature, named after Vyacheslav Ivanovich Lebedev, is an approximation to the surface integral of a function over a three-dimensional sphere. The grid is constructed so to have octahedral rotation and inversion symmetry. The number and location of the grid points together with a ...
In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in ) bounded by C. It is the two-dimensional special case of Stokes' theorem (surface in ). In one dimension, it is equivalent to the fundamental theorem of calculus.
e. In mathematics (particularly multivariable calculus), a volume integral (∭) is an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially important in physics for many applications, for example, to calculate flux densities, or to calculate mass from a corresponding density ...
An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259 [13] 20 examples of periodic solutions to the three-body problem In the 1970s, Michel Hénon and Roger A. Broucke each found a set of solutions that form part of the same family of solutions: the Broucke–Hénon–Hadjidemetriou family.
Slater integrals. In mathematics and mathematical physics, Slater integrals are certain integrals of products of three spherical harmonics. They occur naturally when applying an orthonormal basis of functions on the unit sphere that transform in a particular way under rotations in three dimensions. Such integrals are particularly useful when ...
A volume integral is an integral over a three-dimensional domain or region. When the integrand is trivial (unity), the volume integral is simply the region's volume . [ 14 ] [ 1 ] It can also mean a triple integral within a region D in R 3 of a function f ( x , y , z ) , {\displaystyle f(x,y,z),} and is usually written as: