Introduction to Partial Differential Equations with MATLAB by Jeffery M. Cooper

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Overview The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods.

FORMATHardcover LANGUAGEEnglish CONDITIONBrand New Publisher Description

At the heart of partial differential equations is an unchanging core of material, but the subject is constantly expanding and evolving. This advanced textbook reference is an introduction to partial differential equations covering the traditional subjects of the heat equation, wave equation and Laplace equation in the traditional manner using the method of separation of variables.

Table of Contents

1 Preliminaries.- 1.1 Elements of analysis.- 1.2 Vector spaces and linear operators.- 1.3 Review of facts about ordinary differential equations.- 2 First-Order Equations.- 2.1 Generalities.- 2.2 First-order linear PDE's.- 2.3 Nonlinear conservation laws.- 2.4 Linearization.- 2.5 Weak solutions.- 2.6 Numerical methods.- 2.7 A conservation law for cell dynamics.- 2.8 Projects.- 3 Diffusion.- 3.1 The diffusion equation.- 3.2 The maximum principle.- 3.3 The heat equation without boundaries.- 3.4 Boundary value problems on the half-line.- 3.5 Diffusion and nonlinear wave motion.- 3.6 Numerical methods for the heat equation.- 3.7 Projects.- 4 Boundary Value Problems for the Heat Equation.- 4.1 Separation of variables.- 4.2 Convergence of the eigenfunction expansions.- 4.3 Symmetric boundary conditions.- 4.4 Inhomogeneous problems and asymptotic behavior.- 4.5 Projects.- 5 Waves Again.- 5.1 Acoustics.- 5.2 The vibrating string.- 5.3 The wave equation without boundaries.- 5.4 Boundary value problems on the half-line.- 5.5 Boundary value problems on a finite interval.- 5.6 Numerical methods.- 5.7 A nonlinear wave equation.- 5.8 Projects.- 6 Fourier Series and Fourier Transform.- 6.1 Fourier series.- 6.2 Convergence of Fourier series.- 6.3 The Fourier transform.- 6.4 The heat equation again.- 6.5 The discrete Fourier transform.- 6.6 The fast Fourier transform (FFT).- 6.7 Projects.- 7 Dispersive Waves and the Schrödinger Equation.- 7.1 Oscillatory integrals and the method of stationary phase.- 7.2 Dispersive equations.- 7.3 Quantum mechanics and the uncertainty principle.- 7.4 The Schrödinger equation.- 7.5 The spectrum of the Schrödinger operator.- 7.6 Projects.- 8 The Heat and Wave Equations in Higher Dimensions.- 8.1 Diffusion in higher dimensions.- 8.2 Boundary valueproblems for the heat equation.- 8.3 Eigenfunctions for the rectangle.- 8.4 Eigenfunctions for the disk.- 8.5 Asymptotics and steady-state solutions.- 8.6 The wave equation.- 8.7 Energy.- 8.8 Sources.- 8.9 Boundary value problems for the wave equation.- 8.10 The Maxwell equations.- 8.11 Projects.- 9 Equilibrium.- 9.1 Harmonic functions.- 9.2 The Dirichlet problem.- 9.3 The Dirichlet problem in a rectangle.- 9.4 The Poisson equation.- 9.5 Variational methods and weak solutions.- 9.6 Projects.- 10 Numerical Methods for Higher Dimensions.- 10.1 Finite differences.- 10.2 Finite elements.- 10.3 Galerkin methods.- 10.4 A reaction-diffusion equation.- 11 Epilogue: Classification.- Appendices.- A Recipes and Formulas.- A.1 Separation of variables in space-time problems.- A.2 Separation of variables in steady-state problems.- A.3 Fundamental solutions.- A.4 The Laplace operator in polar and spherical coordinates.- B Elements of MATLAB.- B.1 Forming vectors and matrices.- B.2 Operations on matrices.- B.3 Array operations.- B.4 Solution of linear systems.- B.5 MATLAB functions and mfiles.- B.6 Script mfiles and programs.- B.7 Vectorizing computations.- B.8 Function functions.- B.9 Plotting 2-D graphs.- B.10 Plotting 3-D graphs.- B.11 Movies.- C References.- D Solutions to Selected Problems.- E List of Computer Programs.

Review

"Cooper's book stands out among a host of PDE works. It not only adequately treats traditional core partial differential equation methods but also integrates analytic solutions with numerical schemes through the implementation of MATLAB routines. As an application-oriented book that provides the basic definitions, theorems, and analyses of the solutions, it contains the core topics needed for a sound background in partial differential equations.... One of the book's excellent features is the availability of illustrative and challenging problems, some of which have been cast in the form of MATLAB projects. Such features undoubtedly make this a suitable work for a laboratory component of an introductory PDEs course. Recommended. Undergraduates through faculty."   —Choice

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Long Description

Overview The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. The core consists of solution methods, mainly separation of variables, for boundary value problems with constant coeffi

Review Text

"Cooper's book stands out among a host of PDE works. It not only adequately treats traditional core partial differential equation methods but also integrates analytic solutions with numerical schemes through the implementation of Matlab routines. As an application-oriented book that provides the basic definitions, theorems, and analyses of the solutions, it contains the core topics needed for a sound background in partial differential equations.... One of the book's excellent features is the availability of illustrative and challenging problems, some of which have been cast in the form of MATLAB projects. Such features undoubtedly make this a suitable work for a laboratory component of an introductory PDEs course. Recommended. Undergraduates through faculty."

Review Quote

"Cooper's book stands out among a host of PDE works. It not only adequately treats traditional core partial differential equation methods but also integrates analytic solutions with numerical schemes through the implementation of MATLAB routines. As an application-oriented book that provides the basic definitions, theorems, and analyses of the solutions, it contains the core topics needed for a sound background in partial differential equations.... One of the book's excellent features is the availability of illustrative and challenging problems, some of which have been cast in the form of MATLAB projects. Such features undoubtedly make this a suitable work for a laboratory component of an introductory PDEs course. Recommended. Undergraduates through faculty."

Feature

Includes supplementary material: sn.pub/extras

Details ISBN0817639675 Short Title INTRO TO PARTIAL DIFFERENTIAL Series Applied and Numerical Harmonic Analysis Language English ISBN-10 0817639675 ISBN-13 9780817639679 Media Book Format Hardcover DEWEY 515.353 Edition 1st Pages 541 Imprint Birkhauser Boston Inc Place of Publication Secaucus Country of Publication United States DOI 10.1007/b61666;10.1007/978-1-4612-1754-1 UK Release Date 2000-11-01 AU Release Date 2000-11-01 NZ Release Date 2000-11-01 Author Jeffery M. Cooper Publisher Birkhauser Boston Inc Year 1998 Publication Date 1998-12-18 Alternative 9781461272663 Illustrations XV, 541 p. Audience Undergraduate US Release Date 1998-12-18 Edition Description 1st ed. 1998. Corr. 2nd printing 2000 We've got this

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