Department of Mathematics

MATH336 - Partial Differential Equations

First order partial differential equations, integral surfaces, characteristic curves, initial and boundary conditions, well-posed problems.
Types of second order equations.
Physical models leading to partial differential equations, including Laplace's equation, wave equation and diffusion equation.
Waves and diffusion.
Reflections and sources.
1-dimensional boundary value problems.
Fourier series, maximum principles.
Harmonic functions, Green's identity.
Fundamental solutions, Green's functions, waves in space.
2- and 3-dimensional boundary value problems.
Solution of partial differential equation models in natural sciences.
Eigenvalue problems.
Nonlinear partial differential equations: shock waves, calculus of variations.