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Boundary Value Problems of Applied Mathematics

John L. Troutman and Maurino P. Bautista
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Dhruba Adhikari
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This essentially self-contained book is a great option for a course on elementary partial differential equations with boundary value problems at the undergraduate level. There is no use of the Lebesgue integration theory, the Dirac delta function, or complex integral methods. On the other hand, it does include vibrational methods and contains results that are not commonly found elsewhere at the undergraduate level.

This book deals with both physical and mathematical aspects to emphasize that mathematics helps address the questions that arise from modeling physical processes mathematically. The first part of the book lays out standard material such as Fourier series, linear boundary value problems, derivation of heat and wave equations, separation of variables and series solutions to heat and wave equations, in addition to their physical interpretations. In the second part more sophisticated methods, such as Sturm-Liouville theory and integral transforms, are presented in the context of partial differential equations in two and three spatial dimensions with diverse boundary conditions.

The plentitude of great examples throughout the book has set the stage for amplifying the importance of the applicability of the theories covered. Illustrative examples with figures have greatly added to the clarity of the presentation. Exercises after each section rather than at the end of each chapter is what is commonly preferred at the undergraduate level, and the book has it all. Theorems have been provided with elegant proofs. Applications of the mathematical theory to areas, such as signal processing, earthquake response of building, flood wave and solitons, subsonic versus supersonic flow, signal sampling, band-limited signals, uncertainty principle, electrodynamics, fluid mechanics and acoustics are included. Appendix D with boundary value problems with Maple adds value of the computational aspect to the subject.

In summary, the book is perfectly suitable for a textbook for a one-semester or a relaxed two-semester course on elementary partial differential equations with boundary value problems.

Dhruba Adhikari is Associate Professor of Mathematics at Kennesaw State University, Marietta, Georgia.

The table of contents is not available.