Mathematical Methods for the Natural and Engineering Sciences

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.

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.