Boundary Value Problems of Applied Mathematics: Second Edition (Dover Books on Mathematics)

Addressing both physical and mathematical aspects | this self-contained text on boundary value problems is geared toward advanced undergraduates and graduate students in mathematics. Prerequisites include some familiarity with multidimensional calculus and ordinary differential equations. A brief introductory section precedes the two-part treatment | which begins with coverage of basic theory. Topics include Fourier series of periodic functions | linear boundary value problems | diffusion problems related to the heat equation | steady-state problems involving the potential equation | and propagation problems incorporating the wave equation. The second part focuses on extensions | exploring general second-order linear equations and systems | series methods | integral transform methods | and Sturm–Liouville problems. Problem sets appear throughout the text | along with a substantial section of answers to selected problems. This corrected edition includes a new Preface and an updated Appendix.