Course overview
This course develops fundamental concepts in ordinary differential equations (ODEs) and introduces partial differential equations (PDEs). A range of methods for solving first-order ODEs (using both analytic and numerical techniques) will be developed and their qualitative solution behaviour will be investigated. These concepts will be extended to linear systems of first-order ODEs and second order ODEs. PDEs will be introduced, and the heat and wave equations will be solved using separation of variables.
- Introduction and first order ODEs
- Systems of first order ODEs
- Second order ODEs
- Introduction to partial differential equations (PDEs)
Course learning outcomes
- Classify ODEs, systems of ODEs, and linear PDEs and identify appropriate methods to analyse solutions and behaviours.
- Demonstrate fluency in translating between ODE models and the practical applications they represent.
- Calculate solutions of ODEs and linear PDEs as analytic functions or series solutions.
- Identify ODE solution behaviour, such as bifurcations, fixed points, and qualitative behaviour
- Develop numerical code which utilises in-built solvers and plotting functions to compute and illustrate solutions of ODEs
Degree list
The following degrees include this course