After having finished the course successfully, a student should be able independently to:
- Solve basic first-order linear and quasi-linear PDEs.
- Classify a given second-order linear PDE as either elliptic, parabolic or hyperbolic
- Recognize and solve wave equation, heat equation and Laplace equation
- Predict behavior of the solutions of the above-mentioned PDEs.
The course Partial Differential Equations (PDEs) from Mathematical Physics is a natural extension of the course Ordinary Differential Equations (ODEs). PDEs model a wide range of continuous time processes. The emphasis here is on the description and the building up of understanding of space-dependent processes. A paradigmatic example is the heat-conducting beam: feed heat on one side and the heat spreads over the entire beam. With the help of a simple PDE, someone can now determine exactly how this process takes place.
This course introduces students to the classical subjects of mathematical physics. Here we deal with three classic types of linear second-order PDEs: hyperbolic, parabolic and elliptic. The three named PDEs have a wide range of applications - such as the propagation of waves, thermal diffusion, and electrostatics.