Differential Equations III
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Description
Differential equations describe a wide range of practical problems in areas such as biology, engineering, physical sciences, economics and finance. This course aims to provide students with techniques required to solve classes of ordinary and partial differential equations that commonly occur in applications.
Objective
To extend students' knowledge of the theory and applications of methods for solving ordinary and partial differential equations. To provide students with a range of techniques for solving some classes of ordinary and partial differential equations such as are associated with a wide range of applications in areas such as biology, physics, engineering, economics and finance.
Content
Topics covered are: methods for the solution of systems of linear and non-linear ordinary differential equations; techniques for the solution of two point boundary value problems for second order linear ordinary differential equations with variable coefficients; classification of partial differential equations and the solution of boundary value problems for these equations using the methods of reduction to ordinary differential equations by use of separation of variables, integral transforms, and characteristics.
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| Year |
Semester |
Level |
Units |
| 2012 |
1 |
3 |
3 |
Delivery
36 hours of lectures and tutorials.
Assessment
Ongoing assessment 30%, exam 70%.
Graduate attributes
Linkage past
Prerequisite is MATHS 1007A/B Mathematics I or equivalent. Knowledge of the material in either one of the
subjects APP MTH 2007 Differential Equations II or APP MTH 2000 Differential Equations and Fourier Series II is assumed and knowledge of the material in the subject APP MTH 2006 Methods in Applied Mathematics II is highly desirable.
Linkage present
This course has content useful in many areas of mathematics including mechanics, analysis and mathematical modelling in medicine, finance and industry. It includes material useful in level III applied mathematical courses such as APP MTH 3000 Computational Mathematics III, APP MTH 3017 Waves III, APP MTH 3002 Fluid Mechanics III, APP MTH 3006 Industrial Mathematics III , APP MTH 3004 Mathematical Biology III and APP MTH 3010 Variational Methods and Optimal Control III.
Linkage future
For a student proceeding in the future to Honours or a higher degree in mathematics, the theory and techniques from this course will be useful in many areas.
Restrictions
None.
Recommended text
There is no recommended text. Numerous books in the Barr-Smith Library can be found by checking under differential equations and partial differential equations.
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