Method of characteristics for first and second order partial differential equations, conservation laws and shocks, classification of second order systems and applications.
At the level of Partial Differential Equations, Fritz John
- First Order PDEs; The method of characteristics; Conservation laws and shocks
- Second Order PDEs; Constant coefficients; Boundary conditions; Hyperbolic equations; Parabolic equations; Elliptic equations
- Separation of Variables and Series Solutions
- Green's Functions and Fundamental Solutions