# Analysis of Ordinary Differential Equations

University of Queensland

## Course Description

• ### Course Name

Analysis of Ordinary Differential Equations

• ### Host University

University of Queensland

• ### Location

Brisbane, Australia

Mathematics

• ### Language Level

Taught In English

• ### Prerequisites

MATH1052 or MATH1072

• ### Course Level Recommendations

Lower

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Host University Units

2
• Recommended U.S. Semester Credits
4
• Recommended U.S. Quarter Units
6
• ### Overview

Course Description
ODE's - Systems: variation of constants, fundamental matrix. Laplace transform, transform for systems, transfer function. Stability, asymptotic stability; phase plane analysis.

Course Introduction
MATH2010 will cover the following 2 topics. ( Also for a general outline of the course, read About MATH2010.)
Topic 1. Systems of Ordinary Differential Equations (Kreyszig Chapter 4). Solutions to Homogeneous Linear Systems of ODE's with constant coeffcients using matrices. The Phase Plane for 2-Dimensional linear and some nonlinear systems. Critical Points, linearization and the stability properties of critical points. Nonhomogeneous Linear Systems.

Topic 2. Laplace Transforms (Kreyszig Chapter 6).The Laplace Transform and its Inverse Transform. Linearity, Shifting, Convolution and the use of Partial Fractions. Transforms of Derivatives and Integrals. Use of Laplace Transforms to solve Linear Differential Equations including those involving discontinuous functions such as the Step Function and the Dirac Delta function.

Learning Objectives
After successfully completing this course you should be able to:

1. solve linear systems of ODEs and to be able to interpret their behaviour in the phase plane.
2. find equilibrium solutions to nonlinear systems of ODE's and analyse their stability characteristics.
3. use the Laplace Transform to solve linear ODE's and systems of ODE's with continuous and discontinuous forcing.
4. use the methods described above to analyse systems from Biology, Chemistry, Physics and Engineering (mass spring systems, mixing problems, simple electrical circuit systems, simple chemical rate equations and simple predator prey systems).

Course Contact
2 Hours Lecture, 1 Hour Tutorial

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Some courses may require additional fees.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.