Advanced Mathematics for Applications

A comprehensive guide to the whys, hows and whens of the mathematical methods needed for classical fields.

Andrea Prosperetti (Author)

9780521735872, Cambridge University Press

Paperback, published 6 January 2011

742 pages, 80 b/w illus.
24.7 x 17.3 x 3.6 cm, 1.32 kg

'This book admirably lays down physical and mathematical groundwork, provides motivating examples, gives access to the relevant deep mathematics, and unifies components of many mathematical areas. This sophisticated topics text, which interweaves and connects subjects in a meaningful way, gives readers the satisfaction and the pleasure of putting two and two together.' Laura K. Gross, SIAM Review

The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough presentation.

Preface
To the reader
List of tables
Part I. General Remarks and Basic Concepts: 1. The classical field equations
2. Some simple preliminaries
Part II. Applications: 3. Fourier series: applications
4. Fourier transform: applications
5. Laplace transform: applications
6. Cylindrical systems
7. Spherical systems
Part III. Essential Tools: 8. Sequences and series
9. Fourier series: theory
10. The Fourier and Hankel transforms
11. The Laplace transform
12. The Bessel equation
13. The Legendre equation
14. Spherical harmonics
15. Green's functions: ordinary differential equations
16. Green's functions: partial differential equations
17. Analytic functions
18. Matrices and finite-dimensional linear spaces
Part IV. Some Advanced Tools: 19. Infinite-dimensional spaces
20. Theory of distributions
21. Linear operators in infinite-dimensional spaces
Appendix
References
Index.

Subject Areas: Applied mathematics [PBW], Differential calculus & equations [PBKJ]