# A Guided Tour of Mathematical Methods for the Physical Sciences

Cambridge University Press

Edition: 3, 3/5/2015

EAN 9781107641600, ISBN10: 1107641608

Paperback, 584 pages, 25.3 x 17.7 x 2.5 cm

Language: English

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.