Mathematical Analysis in Engineering: How to Use the Basic Tools

ISBN-13: 9780521587983 / Angielski / Miękka / 1997 / 480 str.

Chiang C. Mei

Opis

Rather than follow the traditional approach of stating mathematical principles and then citing some physical examples for illustration, Professor Mei puts applications at center stage. Beginning with the problem, he finds the mathematics that suits it and closes with a mathematical analysis of the physics. He selects physical examples 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.

Recenzje

'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

Spis treści

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.