Mathematics for Physics
Douban
A Guided Tour for Graduate Students
Michael Stone / Paul Goldbart
overview
An engagingly-written account of mathematical tools and ideas, this book 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 - differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex 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 problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.
contents
Preface
Acknowledgements
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 Groups and group representations
15 Lie groups
16 The geometry of fibre bundles
17 Complex analysis
18 Applications of complex variables
19 Special functions and complex variables
A Linear algebra review
B Fourier series and integrals
References
Index