Boundary Value Problems of Applied Mathematics Second Edition

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.

John L. Troutman is Professor Emeritus of Mathematics, Syracuse University. Maurino Bautista is Professor of Mathematics, Rochester Instititue of Technology.

PrefaceFoundationsPart One: Basic Theory1. Fourier Series of Periodic Functions2. Linear Boundary Value Problems3. Diffusion Problem: The Heat Equation4. Steady-State Problems: The Potential Equation5. Propagation Problems: The Wave EquationPart II: Extensions6. General Second-Order Linear Equations; Systems7. Series Methods8. Integral Transform Methods9. Storm-Liouville ProblemsAppendicesAnswers to Selected ProblemsBibliographyIndexBoundary Value Problems and MAPLE