Introduction to Mathematical Physics

Contents

1. Introduction
2. Some mathematical problems and their solution
   1. Boundary, spectral and evolution problems
   2. Linear boundary problems, integral methods
   3. Boundary problems, variational methods
   4. Linear evolution problems, spectral method
   5. Nonlinear evolution problems, perturbative methods
   6. Evolution, numerical time integration
   7. Particular trajectories and geometry in phase space
   8. Use of change of variables
3. N body problem and matter description
   1. Introduction
   2. Origin of matter
   3. Atoms
   4. Molecules
   5. Crystalline solids
   6. Gas and liquids
   7. Plasmas
   8. Other matter arrangements
   9. Abstract
4. Relativity
5. Electromagnetism
6. Quantum mechanics
7. N body problem in quantum mechanics
8. Statistical physics
9. N body problems and statistical equilibrium
10. Continuous approximation
11. Energy in continuous media

Appendix

1. Measure and integration
2. Groups
3. Vectorial spaces
4. Dual of a vectorial space
5. Topological spaces
6. Dual of a topological space
7. Differentials and derivatives