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More copies of this ISBNOther titles in the Applied and Numerical Harmonic Analysis series:
Introduction to Partial Differential Equations with MATLAB (Applied and Numerical Harmonic Analysis)by J. M. Cooper
Synopses & ReviewsPublisher Comments: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 uptodate 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 selfstudy 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 selfstudy resource for professionals and practitioners.
Book News Annotation:Intended for undergraduate students in math, science, and engineering, this text uses MATLAB software to expand the introduction of differential equations from the core topics of solution techniques for boundary value problems with constant coefficients to topics less common for an introductory text such as nonlinear problems and brief discussions of numerical methods. The Schrodinger equation is dicussed as a dispersive equation and the LaPlace and Poisson equations are treated. Finite difference schemes are used to compute solutions. Some mfiles to implement basic finite difference schemes have been included.
Annotation c. Book News, Inc., Portland, OR (booknews.com) Table of ContentsChapter 1. Preliminaries Chapter 2. FirstOrder Equations: Method of characteristics for linear equations; nonlinear conservation laws; weak solutions; shock waves; numerical methods. Chapter 3. Diffusion: Diffusion on the line; maximum principle; fundamental solution of the heat equation; Burgers' equation; numerical methods. Chapter 4. Boundary Value Problems for the Heat Equation: Separation of variables; eigenfunction expansions; symmetric boundary conditions; longtime behavior. Chapter 5. Waves Again: Gas dynamics; the nonlinear string; linearized model; the linear wave equation without boundaries; boundary value problems on the halfline and finite interval; conservation of energy;numerical methods; nonlinear KleinGordon equation. Chapter 6. Fourier Series and Fourier Transform: Fourier series; Fourier transform and the heat equation; discrete Fourier transform; fast Fourier transform. Chapter 7. Dispersive Waves and the Schrodinger Equation: Method of stationary phase; dispersive equation (group velocity and phase velocity); Schrodinger equation; spectrum of the Schrodinger operator. Chapter 8. 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. Chapter 9. Equilibrium: Harmonic functions; maximum principle; Dirichlet problem in the disk and rectangle; Poisson kernel; Green's functions; variational problems and weak solutions. Chapter 10. Numerical Methods in Higher Dimensions: Finite differences; finite elements; Galerkin methods, A reactiondiffusion equation. Chapter 11. 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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