Course overview
This course aims to equip learners with the skills to apply analytical and numerical techniques to solve complex differential equations, including nonlinear ordinary and partial differential equations. Building upon foundational concepts, the course covers advanced topics such as Sturm-Liouville theory and numerical methods. Through this course, learners will develop critical thinking and problem-solving skills essential for modelling physical scenarios, preparing them for advanced scientific and engineering challenges and fostering a deep comprehension of mathematics and its real-world applications.
- Nonlinear ordinary differential equations
- Green's functions and Sturm-Liouville Theory
- Partial differential equations
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
Availability
Class details
Mawson Lakes
Class number 25915
Section FR01
Size 25
Available 25
Class number 22006
Section WS01
Size 25
Available 25
Adelaide City Campus East
Class number 22007
Section FR01
Size 25
Available 25
Class number 22008
Section WS01
Size 25
Available 25
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