Boundary Value Problems, Fourth Edition

Boundary Value Problems, Fourth Edition, continues to be the leading text on boundary value problems and Fourier series. The author, David Powers, has written a thorough, theoretical overview of solving partial differential equations by the methods of separation of variables. The text is comprised of five comprehensive parts which include: a prerequisite summary of ordinary differential equations, Fourier series, and solving linear partial differential equations by separation of variable methods, by Laplace transform methods, and by numerical methods. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering problems.


* New section on Error Functions in Chapter 2
* New section on Applications of Legendre Polynomials in Chapter 5
* Provides the most comprehensive treatment of The Potential Equation
* Detailed coverage of Laplace Transform
* Presents Numerical Models in Chapter 7
* Addition of about 75 new exercises, including problems from current engineering literature with authentic parameter values

The long awaited revision of David Powers' classic Boundary Value Problems achieves two objectives. The main goal is solving boundary value problems involving partial differential equations. Separation of variables provides a uniform method for attacking important cases of the heat, wave, and potential equations. DiAlembertis solution of the wave equation and the distributed-source solution for the heat equation illustrate other techniques. In addition, there is a chapter on Laplace transform and one on numerical methods, including use of spreadsheets.
The second objective is to tie together the mathematics developed and the learner's physical intuition. This is accomplished by deriving several of the mathematical models, by using some physical reasoning in the mathematical development, by interpreting mathematical results in physical terms, and by studying the heat, wave, and potential equations separately.
"The new edition is an improvement over the third edition. Some of the strengths of the new edition are a clear and casual style f presentation, a large number of worked examples and exercises, numerous graphs and tables that illustrate concepts, and several new applied modeling problems."
--Michael Smiley, Iowa State University
"I enjoyed the clever way in which he motivates the introduction to Sturm-Leouville problems in Chapter 2, showing them to be a natural consequence of the separation if variables method. The new section (2.12) on applications of the error function was a pleasant surprise, as this topic is not addressed in most books."
--Jim Mueller, California Polytechnic State University
"The exercise sets are very good. There are several exercises--especially some recently added-that are excellent examples of more novel topics."
--Lawrence Schovanee, Texas Tech University
"This book will continue to be held in high regard.."
--James V. Herod, Georgia Institute of Technology