Differential Equations

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).