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

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

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

}}~{\boldsymbol {\eta }}\not \in U\\\end{matrix}}\right.} Green's function Kirchhoff integral theorem Lagrange's identity (boundary value problem) Strauss, Walter....

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

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...

function.: 33  Joseph Fourier presented what is now called the Fourier integral theorem in his treatise Théorie analytique de la chaleur in the form: f ( x...

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 ...

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...

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...

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...

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

conductance. In addition to the foundational principles and theorems, several analytical methods are integral to the study of electronics: Network analysis (electrical...

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

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...

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...

Prescott Joule (1818–1889). Kalman filter kelvin kinematics Kirchhoff's circuit laws Kirchhoff's equations laminar flow Laplace transform LC circuit lever...

theory Precipitation hardening Kelvin's circulation theorem Kernel function for solving integral equation of surface radiation exchanges Nonlinear acoustics...

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

These two points of view are related to each other by the fundamental theorem of discrete calculus. The study of the concepts of change starts with their...

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...

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

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...

Where the last equality follows by the mean value theorem for integrals. Using the squeeze theorem and the continuity of ρ {\displaystyle \rho } , one...

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...

linear components (such as resistors, inductors and capacitors) obey Kirchhoff's circuit laws, which leads to a system of linear equations, which can...