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The heat equation predicts that if a hot body is placed in a box of cold water, the temperature of the body will decrease, and eventually (after infinite time, and subject to no external heat sources) the temperature in the box will equalize. | partial differential equation | heat | function | mathematics | parabolic partial differential equation | statistics | Brownian motion | Fokker–Planck equation | diffusion equation | maximum principle | parabolic partial differential equations | random walks | financial mathematics | Riemannian geometry | topology | Richard Hamilton | Ricci flow | Poincaré conjecture | Fourier's law | conservation of energy | specific heat capacity | fundamental theorem of calculus | conservation of energy | Graphical representation of the solution to a 1D heat equation PDE. (View animated version) | isotropic | dimensional | derivatives | thermal conductivity | density | heat capacity | heat conduction | boundary conditions | heat | equilibrium | parabolic partial differential equation | Laplace operator | particle diffusion | action potential | finance | Black-Scholes | Ornstein-Uhlenbeck processes | special relativity | light cone | Idealized physical setting for heat conduction in a rod with homogenous boundary conditions. | | Joseph Fourier | 1822 | separation of variables | eigenvectors | spectral theory | self-adjoint operators | linear operator | orthonormal | inner product | diagonalized | energy | density | Fourier law | matrix | symmetric | positive definite | Green's theorem | specific heat | density | thermal conductivity | Cauchy problem | well-posed problem | one-parameter semigroups | elliptic operator | self-adjoint | spectral theorem | one-parameter semigroup | fundamental solution | Dirac delta function | convolution | Dirichlet | Neumann | Green's function | method of images | Neumann | Dirichlet | linear combination | Jacobi theta function | method of images | Diffusion equation | diffusion | concentration | collective diffusion | probability density function | nonlinear diffusion equation | Brownian motion | probability density function | normal distribution | Schrödinger equation | Schrödinger equation | mass | unit imaginary number | Planck's constant | wavefunction | Schrödinger equation | wavefunction | wavefunction | wavefunction | Schrödinger's equation | modeling | financial mathematics | options | Black–Scholes | differential equation | Crank–Nicolson method | manifolds | Atiyah–Singer index theorem | Riemannian geometry | Heat kernel regularization | Caloric polynomial | Neher–McGrath | divergence theorem | ISBN 0-521-30243-9 | ISBN 0-8218-0772-2 | ISBN 978-0387906096 | Wikimedia Commons | Categories | Diffusion | Heat conduction | Parabolic partial differential equations |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Heat kernel".