Book Description
DCW Industries is pleased to announce publication of a new book on perturbation methods. The motivation for creating the book has been to help restore asymptotic and perturbation analysis to their proper place in an engineer's arsenal of mathematical tools, especially those involved in computer oriented studies.

Several excellent text books on perturbation theory have been written during the past three decades, and most have a common denominator of establishing as much mathematical rigor as possible. This has been done to provide a solid foundation for the approximate methods and "common sense mathematics" used by scientists and engineers for over 100 years. This is certainly a desirable goal that is just as important an issue for the applied mathematician as it is for the engineer.

Since the foundations are now well established, study of these methods by engineers needn't focus on details the mathematician is more appropriately concerned with. Courses on perturbation methods are often referred to by engineers as being "too theoretical." The perceived focus on theory clouds the utility of asymptotic methods.

This book is intended for use by practicing engineers and graduate students who want to master the techniques of asymptotic analysis while leaving formal justification to a more advanced treatise. That is not to say the text is simply a recipe book for asymptotic methods. On the contrary, careful attention focuses on justification of error estimates and explanations are given for why the methods work as well as they do. However, formal proofs are at a minimum. This is similar to mastering integral calculus without learning that there are types of integrals other than the one defined by Riemann.

Layout
Thus, the primary goal of this book is to provide a practical and understandable introduction to the intriguing field of asymptotic methods. The layout of the text is as follows.

• Chapter 1 gives an overview and history, followed by introduction of the order relations and operations with asymptotic expansions.
• Chapter 2 focuses on asymptotic expansion of integrals, including Laplace's method, stationary phase and steepest descent.
• Chapter 3 introduces the general principles of singular perturbation theory, including examples for both ODE's and PDE's.
• Chapter 4 covers the branch of perturbation theory known as multiple-scale analysis, including the Method of Averaging and the WKB method.
• Appendix A summarizes salient properties of the Gamma function.
• Appendix B presents useful concepts for doing contour integrals.
• Appendix C includes useful trigonometric relationships.

Practical examples illustrating how useful asymptotics can be when used in conjunction with computational methods are scattered throughout the text. The text includes an excellent Bibliography, a detailed Index and a large selection of carefully prepared homework problems.

Solutions Manual
The Solutions Manual is typeset and contains detailed solutions to all of the problems in the text. For the more involved problems, solutions are as long as five pages. The solutions manual is available on Compact Disk, which includes a .pdf file that can be viewed and printed with the Adobe Acrobat Reader. Additionally, the solution for each problem is included on the CD in HTML format for use in posting solutions on a Class WWW page.

For University People
The material presented in this book is appropriate for a one-semester, graduate or advanced undergraduate level course. Successful study of this material requires an understanding of basic calculus and proficiency in solving differential equations. The material in Chapter 2 requires a knowledge of complex variable theory, including familiarity with contour integration. If the reader's focus is strictly upon perturbation theory, Chapter 2 can be skipped.

For Practicing Engineers
The book has been written by an engineer for other engineers. The style is intended to clearly explain the powerful concepts that have guided engineering analysis for more than a century. Upon discovering these methods, the computational analyst will gain an outstanding method for understanding complex problems and for determining and controlling numerical error.