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 coupled first-order ODEs and second order ODEs. PDEs will be introduced, and the heat, wave and Laplace equations will be solved using separation of variables.
- Introduction And First Order Odes
- Systems Of First Order Odes
- Second Order Odes
- Partial Differential Equations (Pdes)
Course learning outcomes
- Apply appropriate analytic solution methods to first and second order ODEs, systems of linear ODEs, and constant-coefficient PDEs
- Formulate linear ODE models for practical applications involving one or two dependent variables
- Calculate solutions of linear ODEs and 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