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Summary Of: Laplacian

the Laplacian is at the core of... The Laplacian of a function is also the... Another motivation for the Laplacian appearing in physics is that solutions to... it is common to work with the Laplacian in a variety of different coordinate systems... the spherical Laplacian of a function defined on... can be computed as the ordinary Laplacian of the function extended to... then the Laplacian of the product is given by... being eigenfunctions of the angular part of the Laplacian in spherical coordinates... The Laplacian can be generalized in certain ways to... The Laplacian can also be generalized to an elliptic operator called the... The Laplacian is a common operator in... contains expressions for the Laplacian in terms of Christoffel symbols... Other situations in which a laplacian is defined are... Derivation of the Laplacian in Spherical coordinates...

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Laplace distribution | mathematics | physics | Pierre-Simon de Laplace | differential operator | elliptic operator | modeling | wave propagation | heat flow | Helmholtz equation | electrostatics | fluid mechanics | Laplace's equation | Poisson's equation | quantum mechanics | kinetic energy | Schrödinger equation | functions | harmonic functions | Hodge theory | de Rham cohomology | Euclidean space | divergence | gradient | twice-differentiable | real-valued | partial derivatives | Cartesian coordinates | Ck | open set | trace | Hessian | physical | diffusion | Laplace's equation | equilibrium | net flux | unit normal | divergence theorem | functional | stationary | Green's first identity | fundamental lemma of calculus of variations | Cartesian coordinates | polar coordinates | Cartesian coordinates | cylindrical coordinates | spherical coordinates | polar angle | azimuthal angle | Del in cylindrical and spherical coordinates | Hearing the shape of a drum | | talk page | requests for expansion | non-Euclidean | elliptic | hyperbolic | ultrahyperbolic | Minkowski space | d'Alembert operator | Klein-Gordon equation | wave equation | sign in front of the fourth term | c=1 | Laplace-Beltrami operator | Laplace-Beltrami operator | Riemannian manifold | pseudo-Riemannian manifolds | tensor fields | Laplace-de Rham operator | differential forms | Weitzenböck identity | vector Laplacian | vector fields | discrete Laplace operator | image processing | computer vision | Laplacian of Gaussian | blob detector | scale space | list of formulas in Riemannian geometry | Weyl's lemma (Laplace equation) | Earnshaw's theorem | analysis on fractals | time scale calculus | discrete exterior calculus | ISBN 978-0821807729 | | list of references | external links | inline citations | improve | where appropriate | The Feynman Lectures on Physics | ISBN 978-3540411604 | ISBN 978-0393969979 | Encyclopaedia of Mathematics | ISBN 978-1556080104 | Eric W. Weisstein | MathWorld | Categories | Multivariable calculus | Elliptic partial differential equations | Fourier analysis | Harmonic functions | Differential operators | Articles to be expanded since June 2008 | All articles to be expanded | Articles lacking in-text citations |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Laplacian".