This subject covers various methods of solving systems of ordinary differential equations and partial differential equations. Special functions are studied in the framework of Sturm-Liouville theory, leading naturally into Fourier series and transforms. Laplace transforms are studied in greater depth than in previous subjects. All these methods are applied to solving partial differential equations, providing a capstone for mathematics majors.

Session 2 (60)

Online

Orange Campus

HD/FL

One session

School of Computing and Mathematics

MTH220

- be able to solve simple systems of differential equations;
- be able to analyse the phase plane for linear and nonlinear autonomous systems of differential equations;
- be able to determine the type and stability of the critical points;
- be able to use the gamma, beta and error functions;
- be able to solve ordinary differential equations using series expansions;
- be able to explain Sturm-Liouville theory;
- be able to apply orthogonality to the solution of differential equations;
- be able to apply Laplace transforms to the solution of differential equations;
- be able to calculate Fourier series representing periodic functions;
- be able to extend the techniques of Fourier series to nonperiodic functions by means of Fourier integrals and Fourier transforms;
- be able to solve partial differential equations with given initial and boundary conditions;
- be able to interpret mathematical models and communicate their output to non-mathematical audiences.

- Solution of autonomous systems of differential equations;
- Lyapunov stability;
- Phase plane analysis;
- Series solutions to ordinary differential equations;
- Orthogonal functions;
- Legendre polynomials and series;
- Method of Frobenious for series solutions;
- Bessel's equation;
- Special functions;
- The Laplace transform and its use in solving ordinary and partial differential equations;
- Fourier series, Dirichlet conditions, complex form of Fourier series and Parsevals theorem;
- Fourier transforms;
- Solution of partial differential equations.

The following table summarises the assessment tasks for the online offering of MTH418 in Session 2 2019. Please note this is a guide only. Assessment tasks are regularly updated and can also differ to suit the mode of study (online or on campus).

1

Test 1: systems of odes

3

2

Assignment 1: odes/special functions/series sol'ns

12

3

Test 2: laplace transforms/fourier series

3

4

Assignment 2: laplace transf's/fourier methods/pde

12

5

Final exam

70

*The information contained in the CSU Handbook was accurate at the date of publication: October 2020. The University reserves the right to vary the information at any time without notice.*