Introduction to Partial Differential Equations With Matlab

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9780817639679: Introduction to Partial Differential Equations With Matlab

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- cients in geometrically simple domains. Too often an introductory course focuses exclusively on these core problems and techniques and leaves the student with the impression that there is no more to the subject. Questions of existence, uniqueness, and well-posedness are ignored. In particular there is a lack of connection between the analytical side of the subject and the numerical side. Furthermore nonlinear problems are omitted because they are too hard to deal with analytically. Now, however, the availability of convenient, powerful computational software has made it possible to enlarge the scope of the introductory course. My goal in this text is to give the student a broader picture of the subject. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods. I feel that it is important for the student to see nonlinear problems and numerical methods at the beginning of the course, and not at the end when we run usually run out of time. Furthermore, numerical methods should be introduced for each equation as it is studied, not lumped together in a final chapter.

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Recensione:

"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

Contenuti:

Chapter 1. Preliminaries Chapter 2. First-Order 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; long-time behavior. Chapter 5. 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. 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 reaction-diffusion 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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J M Cooper, Jeffery Cooper
Editore: Birkhauser Boston, Germany (2000)
ISBN 10: 0817639675 ISBN 13: 9780817639679
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Descrizione libro Birkhauser Boston, Germany, 2000. Hardback. Condizione libro: New. 1st ed. 1998. Corr. 2nd printing 2000. 241 x 155 mm. Language: English . Brand New Book. 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- cients in geometrically simple domains. Too often an introductory course focuses exclusively on these core problems and techniques and leaves the student with the impression that there is no more to the subject. Questions of existence, uniqueness, and well-posedness are ignored. In particular there is a lack of connection between the analytical side of the subject and the numerical side. Furthermore nonlinear problems are omitted because they are too hard to deal with analytically. Now, however, the availability of convenient, powerful computational software has made it possible to enlarge the scope of the introductory course. My goal in this text is to give the student a broader picture of the subject. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods. I feel that it is important for the student to see nonlinear problems and numerical methods at the beginning of the course, and not at the end when we run usually run out of time. Furthermore, numerical methods should be introduced for each equation as it is studied, not lumped together in a final chapter. Codice libro della libreria AAU9780817639679

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Jeffery M. Cooper
Editore: Birkhauser Boston 1998-12-18, Berlin (1998)
ISBN 10: 0817639675 ISBN 13: 9780817639679
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Descrizione libro Birkhauser Boston 1998-12-18, Berlin, 1998. hardback. Condizione libro: New. Codice libro della libreria 9780817639679

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Cooper, Jeffery M.
Editore: Birkh?user (2000)
ISBN 10: 0817639675 ISBN 13: 9780817639679
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Descrizione libro Birkh?user, 2000. Condizione libro: New. Offers an introduction to partial differential equations covering the traditional topics within a modern context. This book includes techniques of numerical computation with selected nonlinear topics, including nonlinear first order equations. It discusses the analytical aspects of solutions in an integrated fashion with examples and exercises. Series: Applied and Numerical Harmonic Analysis. Num Pages: 556 pages, biography. BIC Classification: PBKJ; PDE; TBJ. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 242 x 168 x 37. Weight in Grams: 950. . 2000. Corrected. Hardcover. . . . . . Codice libro della libreria V9780817639679

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Jeffery M. Cooper
Editore: Birkhauser Boston, Germany (2000)
ISBN 10: 0817639675 ISBN 13: 9780817639679
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Descrizione libro Birkhauser Boston, Germany, 2000. Hardback. Condizione libro: New. 1st ed. 1998. Corr. 2nd printing 2000. 241 x 155 mm. Language: English . Brand New Book. 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- cients in geometrically simple domains. Too often an introductory course focuses exclusively on these core problems and techniques and leaves the student with the impression that there is no more to the subject. Questions of existence, uniqueness, and well-posedness are ignored. In particular there is a lack of connection between the analytical side of the subject and the numerical side. Furthermore nonlinear problems are omitted because they are too hard to deal with analytically. Now, however, the availability of convenient, powerful computational software has made it possible to enlarge the scope of the introductory course. My goal in this text is to give the student a broader picture of the subject. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods. I feel that it is important for the student to see nonlinear problems and numerical methods at the beginning of the course, and not at the end when we run usually run out of time. Furthermore, numerical methods should be introduced for each equation as it is studied, not lumped together in a final chapter. Codice libro della libreria AAU9780817639679

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Jeffery M. Cooper
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ISBN 10: 0817639675 ISBN 13: 9780817639679
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Descrizione libro Birkhauser Boston. Hardback. Condizione libro: new. BRAND NEW, Introduction to Partial Differential Equations with MATLAB (1st ed. 1998. Corr. 2nd printing 2000), Jeffery M. Cooper, 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- cients in geometrically simple domains. Too often an introductory course focuses exclusively on these core problems and techniques and leaves the student with the impression that there is no more to the subject. Questions of existence, uniqueness, and well-posedness are ignored. In particular there is a lack of connection between the analytical side of the subject and the numerical side. Furthermore nonlinear problems are omitted because they are too hard to deal with analytically. Now, however, the availability of convenient, powerful computational software has made it possible to enlarge the scope of the introductory course. My goal in this text is to give the student a broader picture of the subject. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods. I feel that it is important for the student to see nonlinear problems and numerical methods at the beginning of the course, and not at the end when we run usually run out of time. Furthermore, numerical methods should be introduced for each equation as it is studied, not lumped together in a final chapter. Codice libro della libreria B9780817639679

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Descrizione libro Birkhäuser. Condizione libro: New. Offers an introduction to partial differential equations covering the traditional topics within a modern context. This book includes techniques of numerical computation with selected nonlinear topics, including nonlinear first order equations. It discusses the analytical aspects of solutions in an integrated fashion with examples and exercises. Series: Applied and Numerical Harmonic Analysis. Num Pages: 556 pages, biography. BIC Classification: PBKJ; PDE; TBJ. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 242 x 168 x 37. Weight in Grams: 950. . 2000. Corrected. Hardcover. . . . . Books ship from the US and Ireland. Codice libro della libreria V9780817639679

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Descrizione libro Birkhauser Boston, 1998. HRD. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria BB-9780817639679

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Descrizione libro Birkhäuser, 2000. Condizione libro: New. Codice libro della libreria EH9780817639679

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