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Informationen zum Autor Marcus Pivato is Associate Professor in the Department of Mathematics at Trent University in Peterborough, Ontario. Klappentext This highly visual introductory textbook provides a rigorous mathematical foundation for all solution methods and reinforces ties to physical motivation. Zusammenfassung This highly visual introductory textbook presents an in-depth treatment suitable for undergraduates in mathematics and physics! gradually introducing abstraction while always keeping the link to physical motivation. Designed for lecturers as well as students! downloadable files for all figures! exercises! and practice problems are available online! as are solutions. Inhaltsverzeichnis 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.
