On successful completion of this module, students will be able to:

Give and use basic definitions, e.g. order, linear,type of PDE etc.;

State correctly and apply to examples the basic facts about the Wave Equation in one space dimension: Energy conservation (differential, local and global forms), existence and uniquess of solutions, finite speed of propagation. Solve the initial value problem for given data using the explicit solution;

State correctly and apply to examples the basic facts about the Heat Equation in one space dimension: Maximum Principle (local and global versions), Existence and uniqueness of bounded solutions, smoothing, decay of solutions. Solve the initial value problem for given data using the explicit solution;

State correctly and apply to examples the basic facts about the Laplace Equation in two space dimensions: Maximum Principle (local and global versions), Existence and uniqueness of solutions to the Dirichlet problem. Solve boundary value problems using the Poisson formulae;

Module Content

Module Content;

Classification of partial differential equations

Wave, Heat and Laplace Equations in low dimensions

This module will be examined jointly 2 hour examination in Trinity term. Continuous assessment
will contribute 10% to the final grade for the module at the annual
examination session.