This highly visual introductory textbook provides a rigorous mathematical foundation for all solution methods and reinforces ties to physical motivation.
This highly visual introductory textbook provides a rigorous mathematical foundation for all solution methods and reinforces ties to physical motivation.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Marcus Pivato is Associate Professor in the Department of Mathematics at Trent University in Peterborough, Ontario.
Inhaltsangabe
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.
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.
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.
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.
Rezensionen
'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 PDEs, I will use Pivato's new text.' Kevin R. Vixie, Washington State University
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