Basic concepts for the treatment of ordinary and partial differential equations:
A. Ordinary differential equations:
- first-order differential equations: existence and uniqueness, first-order autonomous differential equations, separation approach, variation of constants, explicitly solvable cases, initial value problems;
- linear differential equations: homogeneous linear systems, matrix-exponential function, variation of constants, differential equations of nth order.
B. Partial differential equations:
- classification and well-posedness of 2nd order partial differential equations;
- wave equation, Poisson's equation, Fourier transform;
- solution methods: separation approach, Fourier transformation.
C. Numerical solution of differential equations:
- single step method (implicit/explicit);
- Runge-Kutta method;
- step size control.