Differential Equations

Differential Equations

1. Ordinary Differential Equations (ODEs)
   i. ODEs: simple cases
   ii. Direct methods for solving linear ODEs
   iii. Linear dynamics via the Green functions
   iv. Linear static problems
   v. Sturm-Liouville (spectral) theory
   vi. Phase space dynamics for conservative and perturbed systems
2. Partial Differential Equations
   i. First-order PDE: method of characteristics
   ii. Classification of linear second-order PDEs
   iii. Elliptic PDEs: methods of Green function
   iv. Waves in a homogeneous media: hyperbolic PDE (bonus)
   v. Diffusion equations
   vi. Boundary value problems: Fourier methods
   vii. Case study: Burgers equation (bonus)