# Advanced Mathematics for Applications

Cambridge University Press, 1/6/2011

EAN 9780521515320, ISBN10: 0521515327

Hardcover, 744 pages, 24.7 x 17.4 x 4 cm

Language: English

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.