# Introduction to Mathematical Physics

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## Contents

- Introduction
- Some mathematical problems and their solution
- Boundary, spectral and evolution problems
- Linear boundary problems, integral methods
- Boundary problems, variational methods
- Linear evolution problems, spectral method
- Nonlinear evolution problems, perturbative methods
- Evolution, numerical time integration
- Particular trajectories and geometry in phase space
- Use of change of variables

- N body problem and matter description
- Relativity
- Electromagnetism
- Quantum mechanics
- N body problem in quantum mechanics
- Statistical physics
- N body problems and statistical equilibrium
- Continuous approximation
- Energy in continuous media

### Appendix

- Measure and integration
- Groups
- Vectorial spaces
- Dual of a vectorial space
- Topological spaces
- Dual of a topological space
- Differentials and derivatives