Course overview
This course aims to enable students to apply analytical and numerical techniques to nonlinear ordinary differential equations, systems of ordinary differential equations, and parabolic, elliptic, and hyperbolic partial differential equations. Students will also use differential equations to model physical scenarios.
Course learning outcomes
- Analyse systems of ordinary differential equations drawn from physical examples, including nonlinear systems, using techniques such as linearisation and stability analysis
- Use Sturm-Liouville theory to analyse and solve linear boundary value problems, including those arising from separation of variables
- Apply analytical techniques to solve parabolic, elliptic, and hyperbolic partial differential equations and evaluate potential finite difference methods
- Compute numerical solutions to parabolic, elliptic, and hyperbolic partial differential equations using finite-difference numerical methods
- Interpret analytical and numerical solutions for ordinary differential equations and partial differential equations, the main component of continuum mathematical models for physical problems
Degree list
The following degrees include this course