MATHS 2102 - Differential Equations II

North Terrace Campus - Semester 1 - 2015

Most "real life" systems that are described mathematically, be they physical, biological, financial or economic, are described by means of differential equations. Our ability to predict the way in which these systems evolve or behave is determined by our ability to model these systems and find solutions of the equations explicitly or approximately. Every application and differential equation presents its own challenges, but there are various classes of differential equations, and for some of these there are established approaches and methods for solving them.
Topics covered are: first order ordinary differential equations (ODEs), higher order ODEs, systems of ODEs, series solutions of ODEs, interpretation of solutions, Fourier analysis and solution of linear partial differential equations using the method of separation of variables.

Most "real life" systems that are described mathematically, be they physical, biological, financial or economic, are described by means of differential equations. Our ability to predict the way in which these systems evolve or behave is determined by our ability to model these systems and find solutions of the equations explicitly or approximately. Every application and differential equation presents its own challenges, but there are various classes of differential equations, and for some of these there are established approaches and methods for solving them.

Topics covered are: first order ordinary differential equations (ODEs), higher order ODEs, systems of ODEs, series solutions of ODEs, interpretation of solutions, Fourier analysis and solution of linear partial differential equations using the method of separation of variables.

Required Resources

Recommended Resources

Online Learning

This course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, and sample solutions. Students should make appropriate use of these resources. Link to MyUni login page: https://myuni.adelaide.edu.au/webapps/login/

Learning & Teaching Modes

This course relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides assessment opportunities for students to gauge their progress and understanding.

Workload

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

Activity

Quantity

Workload Hours

Lectures

36

90

Tutorials

6

24

Assignments

6

42

Total

156

Learning Activities Summary

The course will explore and develop the following.

Basic definitions; Physical examples; Classification of types ODEs

Basic definitions; IVPs; 1st order ODEs; Separable, Linear, Exact

Graphical and numerical methods; directional fields and Eulers method

Existence and Uniqueness for 1st order ODEs; Picard's Method and Theorem

Existence and Uniqueness of IVPs for n-th order linear ODEs; Wronskian test

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