Introduction to Partial Differential Equations with MATLAB

ISBN-10: 0817639675
ISBN-13: 9780817639679
Edition: 1998 (Reprint)
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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  More...

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Book details

List price: $69.95
Copyright year: 1998
Publisher: Springer
Publication date: 11/1/2000
Binding: Hardcover
Pages: 541
Size: 6.50" wide x 9.50" long x 0.75" tall
Weight: 2.046

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 placed in the appropriate physical context. The analytical aspects of solutions are discussed in an integrated fashion with extensive examples and exercises, both analytical and computational. The book is excellent for classroom use and can be used for self-study purposes. Topic and Features: Nonlinear equations including nonlinear conservation laws; Dispersive wave equations and the Schrodinger equation; Numerical methods for each core equation including finite difference methods, finite element methods, and the fast Fourier transform; Extensive use of MATLAB programs in exercise sets. MATLAB m files for numerical and graphics programs available by ftp from this web site. This text/reference is an excellent resources designed to introduce advanced students in mathematics, engineering and sciences to partial differential equations. It is also suitable as a self-study resource for professionals and practitioners.

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

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