Mathematical Analysis in Engineering: How to Use the Basic Tools

This user-friendly 1995 text shows how to use mathematics to formulate, solve and analyse physical problems. Rather than follow the traditional approach of stating mathematical principles and then citing some physical examples for illustration, the book puts applications at centre stage; that is, it starts with the problem, finds the mathematics that suits it and ends with a mathematical analysis of the physics. Physical examples are selected primarily from applied mechanics. Among topics included are Fourier series, separation of variables, Bessel functions, Fourier and Laplace transforms, Green's functions and complex function theories. Also covered are advanced topics such as Riemann–Hilbert techniques, perturbation methods, and practical topics such as symbolic computation. Engineering students, who often feel more awe than confidence and enthusiasm toward applied mathematics, will find this approach to mathematics goes a long way toward a sharper understanding of the physical world.

Table of Contents:
Preface; Achnowledgments; 1. Formulation of physical problems; 2. Classification of equations; 3. One-dimensional waves; 4. Finite domains and separation of variables; 5. Elements of Fourier series; 6. Introduction to Green's functions; 7. Unbounded domains and Fourier transforms; 8. Bessel functions and circular domains; 9. Complex variables; 10. Laplace transform and initial value problems; 11. Conformal mapping and hydrodynamics; 12. Riemann–Hilbert problems in hydrodynamics and elasticity; 13. Perturbation methods - the art of approximation; 14. Computer algebra for perturbation analysis; Appendices; Bibliography; Index.

Review :
'The strength of the book lies in its wealth of applications. All too often books on this topic focus on mathematical techniques while paying only a lip service to applications. Professor Mei set out to give engineering applications a larger 'share of the spotlight'. Numerous examples are worked in the text, and additional applications can be found in the exercises. The problems are drawn from mechanics; they include problems such as vibrating strings, the bending of beams, problems in diffusion, and heat conduction. The author has also included many problems from the geosciences.' Jurgen Gerlach, SIAM Review 'All-in-all, this is an excellent book with a readable style. The mathematical analysis is clear … The examples and illustrations are well-chosen and as simple as can be without being trivial. They are also practical and very diverse.' J. A. Hudson, Journal of Fluid Mechanics