Linear partial differential equations and Fourier theory / Marcus Pivato.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Suggested 12-week syllabus -- Heat and diffusion -- Waves and signals -- Quantum mechanics -- Linear partial differential equations -- Classification of PDEs and problem types -- Some functional analysis -- Fourier sine series and cosine series -- Real Fourier series and complex Fourier series -- Multidimensional Fourier series -- Proofs of the Fourier convergence theorems -- Boundary value problems on a line segment -- Boundary value problems on a square -- Boundary value problems on a cube -- Boundary value problems in polar coordinates -- Eigenfunction methods on arbitrary domains -- Separation of variables --Impulse-response methods -- Applications of complex analysis -- Fourier transforms -- Fourier transform solutions to PDEs -- Appendix A: Sets and functions -- Appendix B: Derivatives--notation -- Appendix C: Complex numbers -- Appendix D: Coordinate systems and domains -- Appendix E: Vector calculus -- Appendix F: Differentiation of function series -- Appendix G: Differentiation of integrals -- Appendix H: Taylor polynomials.

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.