0. Dynamical and complex systems. Waves, diffusion, shocks, patterns.
1. Linear operators and Ordinary Differential Equations. Strurm-Liuville operator. Spectral analysis.
2. Partial Differential Equations.
a. Linear second order. Elliptic, parabolic, hyperbolic. Examples from physics. Green function approach.
b. First order – integration over characteristics.
3. Bonus: Perturbation Theory.
4. Bonus: Asymptotic methods (matched-asymptotic).