MTH418 Topics In Calculus (8)

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.

Availability

Session 2 (60)
Online
Orange Campus

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.

Subject Information

Grading System

HD/FL

Duration

One session

School

School of Computing and Mathematics

Prerequisites

MTH220

Learning Outcomes

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;
  • be able to interpret mathematical models and communicate their output to non-mathematical audiences.

Syllabus

This 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.

Indicative Assessment

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).

Item Number
Title
Value %
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: July 2020. The University reserves the right to vary the information at any time without notice.

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