Linear Partial Differential Equations and Fourier Theory

ISBN: 9780521199704 出版年：2010 页码：631 Marcus Pivato Cambridge University Press

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.