The course will introduce students to the most important features of Partial Differential Equations (PDE), from an Applied Mathematics perspective. The student will become familiar with the most important PDEs in Engineering and Physics and will become familiar with basic techniques for solving them. The student will also become familiar with numerical methods for solving PDEs, their scope and difficulties.
The course will present the following topics in partial differential equations, with additional topics and examples presented at the lecturer's discretion.
Classification of PDEs (elliptic, parabolic and hyperbolic)
Boundary conditions, method of characteristics, shocks and discontinuities
Modelling of physics and engineering problems with PDEs
Maxwell¿s system of equations
Green functions for linear PDEs and integral equations
Separation of variables
Coordinate systems and the origin of many special functions