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.
About the Author
John L. Troutman is Professor Emeritus of Mathematics, Syracuse University. Maurino Bautista is Professor of Mathematics, Rochester Instititue of Technology.
Table of Contents
Part One: Basic Theory
1. Fourier Series of Periodic Functions
2. Linear Boundary Value Problems
3. Diffusion Problem: The Heat Equation
4. Steady-State Problems: The Potential Equation
5. Propagation Problems: The Wave Equation
Part II: Extensions
6. General Second-Order Linear Equations; Systems
7. Series Methods
8. Integral Transform Methods
9. Storm-Liouville Problems
Answers to Selected Problems
Boundary Value Problems and MAPLE