基本説明
Discusses in detail the mathematical skills needed throughout common graduate level courses in physics.
Full Description
Going beyond standard mathematical physics textbooks by integrating the mathematics with the associated physical content, this book presents mathematical topics with their applications to physics as well as basic physics topics linked to mathematical techniques. It is aimed at first-year graduate students, it is much more concise and discusses selected topics in full without omitting any steps. It covers the mathematical skills needed throughout common graduate level courses in physics and features around 450 end-of-chapter problems, with solutions available to lecturers from the Wiley website.
Contents
1. Vectors
2. Tensors and Matrices
3. Hamiltonian Mechanics
4. Coupled Oscillators and Normal Modes
5. Stretched String
6. Vector Calculus and the del Operator
7. Electromagnetic Waves
8. Fluid Dynamics
9. Irreversible Processes
10. The Entropy
11. Thermodynamic Inequalities
12. Probability, Statistics and Density
13. Liouville Equation
14. Generalized Vectors and Linear Operators
15. Quantum Mechanics
16. Fourier Series and Transforms
17. Angular Momentum
18. Spin Angular Momentum
19. Time-dependent Perturbation Theory
20. Laplace Transformation
21. Quantum Harmonic Oscillator
22. Permutation Group
23. Quantum Statistics
24. The Free-Electron Model
25. Bose-Einstein Condensation
26. Magnetic Susceptibility
27. Theory of Variations
28. Second Quantization
29. Quantum Statistics of Composites
30. Superconductivity
31. Complex Numbers
32. Analyticity and Cauchy-Riemann Equations
33. Cauchy's Fundamental Theorem
34. Laurent Series
35. Multivalued Functions
36. Residue Theorem and its Applications
Appendices
A. Representation-Independence of Poisson Brackets
B. Proof of the Convolution Theorem
C. Statistical Weight of the Landau States
D. Useful Formulas
