## Partial differential equations for scientists and engineersPractical text shows how to formulate and solve partial differential equations. Coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, numerical and approximate methods. Solution guide available upon request. 1982 edition. |

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### Contents

Introduction to Partial Differential Equations | 3 |

DiffusionType Problems Parabolic Equations | 11 |

Boundary Conditions for DiffusionType Problems | 19 |

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32 other sections not shown

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### Common terms and phrases

a2uxx approximation basic boundary conditions boundary-value problems canonical form circle conformal mappings convection coordinates cosine transform curve D'Alembert solution depends diagram diffusion Dirichlet problem drumhead eigenfunctions eigenvalues elliptic Euler-Lagrange equation example Figure find the solution finite sine finite-difference flux formula Fourier series Fourier transform frequency function f(x given gives graph Green's function grid points heat equation heat flow hence homogeneous hyperbolic IBVP initial conditions initial-value problem inside integral transforms interior Dirichlet problem interpretation inverse Laplace transform Laplace's equation Laplacian linear Mathematical minimizing function Monte Carlo method nonhomogeneous nonlinear Note one-dimensional original problem parabolic partial derivatives Partial Differential Equations PDE V2u physical potential PURPOSE OF LESSON reader separation of variables simple sine and cosine sine transform solution u(x,t solve PDE steady-state STEP substitute technique velocity wave equation wino z-plane zero