Boundary Value Problems

by David L. Powers

Boundary Value Problems is a text material on partial differential equations that teaches solutions of boundary value problems. The book also aims to build up intuition about how the solution of a problem should behave. The text consists of seven chapters. Chapter 1 covers the important topics of Fourier Series and Integrals. The second chapter deals with the heat equation, introducing separation of variables. Material on boundary conditions and Sturm-Liouville systems is included here. Chapter 3 presents the wave equation; estimation of eigenvalues by the Rayleigh quotient is mentioned briefly. The potential equation is the topic of Chapter 4, which closes with a section on classification of partial differential equations. Chapter 5 briefly covers multidimensional problems and special functions. The last two chapters, Laplace Transforms and Numerical Methods, are discussed in detail. The book is intended for third and fourth year physics and engineering students.

Genres: Mathematics, Nonfiction

248 pages, Paperback

First published December 1, 1979

Reviews

[Lukasz Pruski · Rating 5 out of 5]

I have been teaching undergraduate Partial Differential Equations for 31 years. I have tried various textbooks, including classics such as, for example, Brown and Churchill, and other well-known texts, for instance, by Colton, Jeffrey, Pinsky, Duchateu and Zachman, and others. After each such experiment I come back to David L. Powers. It is a perfect undergraduate text on boundary value problems, Fourier methods, and partial differential equations. The level is just right - not too difficult yet not too trivial. The selection of problems is great, with varying level of difficulty. The author's writing is clear and understandable even by medium-level undergraduates.

I have just reread the textbook in preparation for my spring course, so I am listing the date of finishing as December 20, 2014, although the first time I read this book was in 1989.

Of course, the text would be too low level for a graduate course, but it provides a wonderfully clear introduction to Fourier methods. Highly recommended!

Five stars in its particular niche.