MTH418 Topics In Calculus (8)
CSU Discipline Area: Mathematics and Statistics (MASTA)
Duration: One session
Abstract:
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.
+ Subject Availability Modes and Locations
| Session 2 | |
|---|---|
| Distance | Orange |
Continuing students should consult the SAL for current offering details: MTH418
Where differences exist between the Handbook and the SAL, the SAL should be taken as containing the correct subject offering details.
Prerequisite(s):
Objectives:
Upon successful completion of this subject, students should:
- 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.
Syllabus:
The subject will cover the following topics:
- 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 information contained in the 2013 CSU Handbook was accurate at the date of publication: 24 April 2013. The University reserves the right to vary the information at any time without notice.