Mechanics II

This course consists principally of an introduction to the theory and applications of partial differential equations. Topics covered include the heat equation, the wave equation, Laplace's equation, and a brief introduction to the special theory of relativity.

Learning Outcomes
1. formulate a well-posed problem for the heat equation;
2. solve some initial boundary value problems for the heat equation using the method of separation of variables;
3. find the general solution to the one-dimensional wave equation using characteristic variables;
4. construct solutions to the one-dimensional wave equation on an infinite and semi-infinite domain using characteristic variables;
5. construct separable variable solutions to the wave equation;
6. construct separable variable solutions to Laplace's equation;
7. state Einstein's two postulates of special relativity;
8. perform simple calculations in special relativity involving time dilation, length contraction, velocity transformations, energy and momentum.