Linear Partial Differential Equations and Fourier Theory - Marcus Pivato

Linear Partial Differential Equations and Fourier Theory

(Autor)

Buch | Hardcover
630 Seiten
2010
Cambridge University Press (Verlag)
978-0-521-19970-4 (ISBN)
124,65 inkl. MwSt
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.
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.

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

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.

Erscheint lt. Verlag 7.1.2010
Zusatzinfo Worked examples or Exercises; 75 Halftones, unspecified; 75 Line drawings, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 178 x 254 mm
Gewicht 1360 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Naturwissenschaften Physik / Astronomie
ISBN-10 0-521-19970-0 / 0521199700
ISBN-13 978-0-521-19970-4 / 9780521199704
Zustand Neuware
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