A Guided Tour of Mathematical Methods for the Physical Sciences

This completely revised edition provides a comprehensive tour of the mathematical knowledge and techniques needed by students across the physical sciences.

Roel Snieder (Author), Kasper van Wijk (Author)

9781107641600, Cambridge University Press

Paperback / softback, published 5 March 2015

579 pages, 153 b/w illus. 10 tables
25.4 x 17.8 x 2.5 cm, 1.22 kg

'The first and second editions of this gem of a volume were received with praise such as 'a delight of a book', 'a fantastic set of physical problems that opens the gate to the understanding of mathematical physics', and 'a refreshing alternative approach', among many others. It is difficult to find better words to describe the third edition … It is student-friendly not only in its clarity and elegance of style … The volume is both a finely honed learning tool and a good reference for most of the mathematics that a geophysicist might encounter in practice … In short, here is a book that no practicing geophysicist … should be without.' Sven Treitel, The Leading Edge

Mathematical methods are essential tools for all physical scientists. This book provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students across the physical sciences. In contrast to more traditional textbooks, all the material is presented in the form of exercises. Within these exercises, basic mathematical theory and its applications in the physical sciences are well integrated. In this way, the mathematical insights that readers acquire are driven by their physical-science insight. This third edition has been completely revised: new material has been added to most chapters, and two completely new chapters on probability and statistics and on inverse problems have been added. This guided tour of mathematical techniques is instructive, applied, and fun. This book is targeted for all students of the physical sciences. It can serve as a stand-alone text, or as a source of exercises and examples to complement other textbooks.

1. Introduction
2. Dimensional analysis
3. Power series
4. Spherical and cylindrical coordinates
5. Gradient
6. Divergence of a vector field
7. Curl of a vector field
8. Theorem of Gauss
9. Theorem of Stokes
10. The Laplacian
11. Scale analysis
12. Linear algebra
13. Dirac delta function
14. Fourier analysis
15. Analytic functions
16. Complex integration
17. Green's functions: principles
18. Green's functions: examples
19. Normal modes
20. Potential-field theory
21. Probability and statistics
22. Inverse problems
23. Perturbation theory
24. Asymptotic evaluation of integrals
25. Conservation laws
26. Cartesian tensors
27. Variational calculus
28. Epilogue on power and knowledge.

Subject Areas: Maths for engineers [TBJ], Maths for scientists [PDE], Mathematics & science [P]