This second edition provides a broad range of methods and concepts required for the analysis and solution of equations which arise in the modeling of phenomena in the natural, engineering, and applied mathematical sciences. It may be used productively by both undergraduate and graduate students, as well as others who wish to learn, understand, and apply these techniques. Detailed discussions are also given for several topics that are not usually included in standard textbooks at this level of presentation: qualitative methods for differential equations, dimensionalization and scaling, elements of asymptotics, difference equations and several perturbation procedures. Further, this second edition includes several new topics covering functional equations, the Lambert–W function, nonstandard sets of periodic functions, and the method of dominant balance. Each chapter contains a large number of worked examples and provides references to the appropriate books and literature.
Sample Chapter(s)
Chapter 1: Introduction (230 KB)
Chapter 2: Trigonometric Relations and Fourier Analysis (370 KB)
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Contents:
- Introduction
- Trigonometric Relations and Fourier Analysis
- Gamma, Beta, Zeta and Other Named Functions
- Qualitative Methods for Ordinary Differential Equations
- Difference Equations
- Sturm-Liouville Problems
- Special Functions and Their Properties
- Perturbation Methods for Oscillatory Systems
- Approximations of Integrals and Sums
- Some Important Nonlinear Partial Differential Equations
- Generalized Periodic Functions
- Functional Equations
- Miscellaneous Topics
- Appendix A: Mathematical Relations
- Appendix B: Asymptotics Expansions
Readership: Undergraduate and graduate students, and researchers studying or using mathematical techniques and methods.
Review of the First Edition:
"The reader shall also benefit from numerous exercises which conclude each chapter along with helpful bibliographic comments and extensive lists of recommended literature ... Most chapters can be studied independently of each other. This allows one to select material appropriate for the one semester course whereas all the topics can be presented in one year. The text contains enough material to support courses on advanced engineering mathematics, mathematical methods or mathematical physics and thus is warmly recommended as supplementary reading. The book shall also prove very helpful to specialists who look for a well-written introduction to basic mathematical techniques used for solving applied problems."
Zentralblatt MATH