Linear Partial Differential Equations and Fourier Theory

by Marcus Pivato

Overview

Do you want a rigorous book that remembers where PDEs come from and what they look like? This highly visual introduction to linear PDEs and initial/boundary value problems connects the math to physical reality, all the time providing a rigorous mathematical foundation for all solution methods. Readers are gradually introduced to abstraction – the most powerful tool for solving problems – rather than simply drilled in the practice of imitating solutions to given examples. The book is therefore ideal for students in mathematics and physics who require a more theoretical treatment than given in most introductory texts. Also designed with lecturers in mind, the fully modular presentation is easily adapted to a course of one-hour lectures, and a suggested 12-week syllabus is included to aid planning. Downloadable files for the hundreds of figures, hundreds of challenging exercises, and practice problems that appear in the book are available online, as are solutions.

Product Details

ISBN-13:	9780521136594
Publisher:	Cambridge University Press
Publication date:	01/07/2010
Edition description:	New Edition
Pages:	630
Product dimensions:	6.70(w) x 9.60(h) x 1.30(d)

About the Author

Marcus Pivato is Associate Professor in the Department of Mathematics at Trent University in Peterborough, Ontario.

Table of Contents

Preface; Notation; What's good about this book?; Suggested twelve-week syllabus; Part I. Motivating Examples and Major Applications: 1. Heat and diffusion; 2. Waves and signals; 3. Quantum mechanics; Part II. General Theory: 4. Linear partial differential equations; 5. Classification of PDEs and problem types; Part III. Fourier Series on Bounded Domains: 6. Some functional analysis; 7. Fourier sine series and cosine series; 8. Real Fourier series and complex Fourier series; 9. Mulitdimensional Fourier series; 10. Proofs of the Fourier convergence theorems; Part IV. BVP Solutions Via Eigenfunction Expansions: 11. Boundary value problems on a line segment; 12. Boundary value problems on a square; 13. Boundary value problems on a cube; 14. Boundary value problems in polar coordinates; 15. Eigenfunction methods on arbitrary domains; Part V. Miscellaneous Solution Methods: 16. Separation of variables; 17. Impulse-response methods; 18. Applications of complex analysis; Part VI. Fourier Transforms on Unbounded Domains: 19. Fourier transforms; 20. Fourier transform solutions to PDEs; Appendices; References; Index.

Editorial Reviews

"I love this bare-handed approach to PDEs. Pivato has succeeded in creating a deeply engaging introductory PDE text; confidence building hands-on work and theory are woven together in a way that appeals to the intuition. Add to that the truly reasonable price, and you have the hands down winner in the field of introductory PDE books. The next time I teach introductory PDE's, I will use Pivato's new text."
Kevin R. Vixie, Washington State University

"The book comprises a well-organized exposition of a lot of useful material..."
Gerald B. Folland, SIAM Review

From the Publisher