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Kirchhoff's integral theorem (sometimes referred to as the Fresnel–Kirchhoff integral theorem) [1] is a surface integral to obtain the value of the solution of the homogeneous scalar wave equation at an arbitrary point P in terms of the values of the solution and the solution's first-order derivative at all points on an arbitrary closed surface (on which the integration is performed) that ...
Kirchhoff's integral theorem, sometimes referred to as the Fresnel–Kirchhoff integral theorem, [3] uses Green's second identity to derive the solution of the homogeneous scalar wave equation at an arbitrary spatial position P in terms of the solution of the wave equation and its first order derivative at all points on an arbitrary closed surface as the boundary of some volume including P.
The Kirchhoff–Helmholtz integral combines the Helmholtz equation with the Kirchhoff integral theorem [1] to produce a method applicable to acoustics, [2] seismology [3] and other disciplines involving wave propagation.
In fluid dynamics, the Kirchhoff equations, named after Gustav Kirchhoff, describe the motion of a rigid body in an ideal fluid. = + + +, = + +, = (~ +) = ^, = ^ where and are the angular and linear velocity vectors at the point , respectively; ~ is the moment of inertia tensor, is the body's mass; ^ is a unit normal vector to the surface of the body at the point ; is a pressure at this point ...
Kirchhoff showed that in many cases, the theorem can be approximated to a simpler form that is equivalent to the formation of Fresnel's formulation. [3] For an aperture illumination consisting of a single expanding spherical wave, if the radius of the curvature of the wave is sufficiently large, Kirchhoff gave the following expression for K(χ ...
Fubini's theorem (integration) Fubini's theorem on differentiation (real analysis) Fuchs's theorem (differential equations) Fuglede's theorem (functional analysis) Full employment theorem (theoretical computer science) Fulton–Hansen connectedness theorem (algebraic geometry) Fundamental theorem of algebra (complex analysis)
Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.
Kirchhoff's laws, a group of laws of physics (in thermodynamics, electrical circuits, spectroscopy, and fluid mechanics) named for Gustav Kirchhoff; Kirchhoff's theorem, in graph theory, a theorem concerning the number of "spanning trees" in a graph, named for Gustav Kirchhoff; Kirchhof (disambiguation)