Mathematics for Physics: A Guided Tour for Graduate Students – Michael Stone – 1st Edition


An engagingly-written account of mathematical tools and ideas, this provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – and equations, and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and variables.

The authors’ exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study.

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Table of Contents

1. Calculus of variations
2. Function spaces
3. Linear ordinary differential equations
4. Linear differential operators
5. Green functions
6. Partial differential equations
7. The mathematics of real waves
8. Special functions
9. Integral equations
10. Vectors and tensors
11. Differential calculus on manifolds
12. Integration on manifolds
13. An introduction to differential topology
14. Group and group representations
15. Lie groups
16. The geometry of fibre bundles
17. Complex analysis I
18. Applications of complex variables
19. Special functions and complex variables

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