## Description

Mathematical methods are essential tools for all physical scientists. This novel textbook provides a comprehensive guided tour of the mathematical knowledge and techniques needed by students in this area. In contrast to more traditional textbooks, all the material is presented in the form of problems. Within these problems the basic mathematical theory and its physical applications are very well integrated. In this way the mathematical insights that the students acquire are driven by their physical insight. Topics that are covered include vector calculus (div, grad, curl, Laplacian), linear algebra, Fourier analysis, scale analysis, Green’s functions, normal modes, tensor calculus and perturbation theory.

This book can be used by undergraduates or by lower-level graduate students in the physical sciences. It can serve as a stand-alone text, or as a source of problems and examples to complement other textbooks. This guided tour of mathematical techniques is instructive, applied, and even fun.

**Features**

• All the material is presented in the form of problems

• Mathematical insights are gained by getting the reader to develop answers themselves

• Many applications of the mathematics are given

**Reviews**

‘… a splendid book, quite a delight to see mathematical models from a different perspective … treatment is so smooth that it is hard to know at any instant whether one is learning new tools or assimilating the applications to interesting examples… excellent.’ (Donald de Cogan, International Journal of Numerical Modelling)

…This book integrates mathematical theory with a wide range of applications in physics … it could be a stand-alone textbook for an upper-year undergraduate course, but would also provide a good accompaniment to undergraduate maths courses. Teachers may also be more generally interested in this book for its many examples that may serve as useful supplements to physics or geophysics courses …I can highly recommend this book to students and teachers in the physical sciences. (Mike Kendall, Astronomy & Geophysics)

…Guided by Roel Sneider’s textbook, learning mathematical methods can be fun … I highly recommend [it]. ( Francois Primeau, EOS)

**Table of Contents**

1. Introduction;

2. Power series;

3. Spherical and cylindrical coordinates;

4. The gradient;

5. The divergence of a vector field;

6. The curl of a vector field;

7. The theorem of Gauss;

8. The theorem of Stokes;

9. The Laplacian;

10. Conservation laws;

11. Scale analysis;

12. Linear algebra;

13. The 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 theory;

21. Cartesian tensors;

22. Perturbation theory;

23. Epilogue, on power and knowledge; References.

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