Kirchhoff's integral theorem (sometimes referred to as the Fresnel–Kirchhoff integral theorem) is a surface integral to obtain the value of the solution...

the Fresnel–Kirchhoff diffraction formula. Kirchhoff's integral theorem, sometimes referred to as the Fresnel–Kirchhoff integral theorem, uses Green's...

The Kirchhoff–Helmholtz integral combines the Helmholtz equation with the Kirchhoff integral theorem to produce a method applicable to acoustics, seismology...

another temperature. Kirchhoff also worked in the mathematical field of graph theory, in which he proved Kirchhoff's matrix tree theorem. Gesammelte Abhandlungen...

1882, Gustav Kirchhoff analyzed Fresnel's theory in a rigorous mathematical formulation, as an approximate form of an integral theorem.: 375  Very few...

divergence of a scalar times a vector on the RHS. Green's function Kirchhoff integral theorem Lagrange's identity (boundary value problem) Strauss, Walter....

calculus in integral form and differential form; both are equivalent since they are related by the divergence theorem, also called Gauss's theorem. Each of...

derivatives and integrals in alternative calculi List of equations List of fundamental theorems List of hypotheses List of inequalities Lists of integrals List of...

distributions. Joseph Fourier presented what is now called the Fourier integral theorem in his treatise Théorie analytique de la chaleur in the form: f ( x...

classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities (sources)...

Castigliano's theorems do not apply to 2 − D {\displaystyle 2-D} and 3 − D {\displaystyle 3-D} problems. The exception is the Kirchhoff plate, m = 2 ...

fundamental theorem of calculus, that integrals can be computed using any of a function's antiderivatives. The first full proof of the fundamental theorem of calculus...

decomposition Helmholtz–Leray decomposition Helmholtz equation Kirchhoff–Helmholtz integral Helmholtz flow Helmholtz free energy Helmholtz free entropy Kelvin–Helmholtz...

equivalent: An "integral form" and a "differential form". The forms are exactly equivalent, and related by the Kelvin–Stokes theorem (see the "proof"...

Im is the identity matrix of dimension m. The discrete Laplacian (or Kirchhoff matrix) is obtained from the oriented incidence matrix B(G) by the formula...

of the differential and integral formulations are a consequence of the Gauss divergence theorem and the Kelvin–Stokes theorem. According to the (purely...

 108–110. Retrieved 3 November 2023. Siegel 1976 Kirchhoff 1860a Kirchhoff 1860b Schirrmacher 2001 Kirchhoff 1860c Planck 1914, p. 11 Milne 1930, p. 80 Rybicki...

two forms, a differential form and an integral form. These forms are equivalent due to the divergence theorem. The name "Gauss's law for magnetism" is...

by Clemens Fuchs, with a commentary and the article Integral points on curves: Siegel's theorem after Siegel's proof by Clemens Fuchs and Umberto Zannier...

1811 it is clear that he knew the "fundamental theorem of complex analysis" – Cauchy's integral theorem – and understood the notion of complex residues...

used. Substituting this back into the volume integral and another application of the divergence theorem again. This yields − 1 2 ∫ V ∂ ∂ x k ( ∑ i u i...

solution to Poisson's equation, and has a zero path integral. See gradient theorem. The integral equation is true for any path ∂Σ through space, and any...

short circuit – open circuit Kirchhoff's current law – Kirchhoff's voltage law. KVL and KCL Thévenin's theorem – Norton's theorem The use of duality in circuit...

number theory, for example proving Fermat's two-square theorem and Lagrange's four-square theorem, and similar results for 6 and 8 squares. His other work...

of stress are required, such as the Piola–Kirchhoff stress tensor, the Biot stress tensor, and the Kirchhoff stress tensor. According to the principle...

specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is...

physiologischen Optik of 1856 as cited by Gustav Kirchhoff and by Max Planck. As cited by Kirchhoff in 1860, the principle is translated as follows: A...

polarisation and fluorescence. As a mathematician, he popularised "Stokes' theorem" in vector calculus and contributed to the theory of asymptotic expansions...

example, the Aharonov–Bohm effect depends on a line integral of A around a closed loop, and this integral is not changed by A → A + ∇ ψ . {\displaystyle \mathbf...

\mathbf {l} .} By Stokes's theorem, the closed line integral of H·dl around a contour is equal to the open surface integral of curl H·dA across the surface...