Introduction to Partial Differential Equations with MATLAB

Name: Introduction to Partial Differential Equations with MATLAB
Availability: InStock
ISBN: 9780817639679

ISBN-10: 0817639675

ISBN-13: 9780817639679

Edition: 1998 (Reprint)

Authors: Jeffery M. Cooper

List price: $84.99

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Description:

The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. Introduction to Partial Differential Equations with MATLAB is a careful integration of traditional core topics with modern topics, taking full advantage of the computational power of MATLAB to enhance the learning experience. This advanced text/reference is an introduction to partial differential equations covering the traditional topics within a modern context. To provide an up-to-date treatment, techniques of numerical computation have been included with carefully selected nonlinear topics, including nonlinear first order equations. Each equation studied is…

Book details

List price: $84.99
Copyright year: 1998
Publisher: Birkhï¿½user Boston
Publication date: 12/18/1998
Binding: Hardcover
Pages: 541
Size: 6.10" wide x 9.25" long x 0.45" tall
Weight: 2.046
Language: English




Preliminaries



First-Order Equations:Method of characteristics for linear equations


nonlinear conservation laws


weak solutions


shock waves


numerical methods



Diffusion:Diffusion on the line


maximum principle


fundamental solution of the heat equation


Burgers' equation


numerical methods



Boundary Value Problems for the Heat Equation:Separation of variables


eigenfunction expansions


symmetric boundary conditions


long-time behavior



Waves Again:Gas dynamics


the nonlinear string


linearized model;the linear wave equation without boundaries


boundary value problems on the half-line and finite interval


conservation of energy;numerical methods


nonlinear Klein-Gordon equation



Fourier Series and Fourier Transform: Fourier series


Fourier transform and the heat equation


discrete Fourier transform


fast Fourier transform



Dispersive Waves and the Schrodinger Equation:Method of stationary phase


dispersive equation (group velocity and phase velocity)


Schrodinger equation


spectrum of the Schrodinger operator



The Heat and Wave Equations in Higher Dimensions: Fundamental solution of heat equation


eigenfunctions for the disk and rectangle


Kirchoff's formula for the wave equation


nodal curves


conservation of energy


the Maxwell equations



Equilibrium: Harmonic functions


maximum principle


Dirichlet problem in the disk and rectangle


Poisson kernel


Green's functions


variational problems and weak solutions



Numerical Methods in Higher Dimensions:Finite differences


finite elements


Galerkin methods, A reaction-diffusion equation



Epilogue: Classification


Appendix A: Recipes and Formulas


Appendix B: Elements of MATLAB


Appendix C: References


Appendix D: Solutions to Selected Problems


Appendix E: List of Computer Programs


Index