Unit name | Ordinary Differential Equations 2 |
---|---|
Unit code | MATH20101 |
Credit points | 20 |
Level of study | I/5 |
Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
Unit director | Dr. Slastikov |
Open unit status | Not open |
Pre-requisites |
MATH11002 and MATH11003 |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Differential equations are a natural means to express the laws that govern a wide variety of systems: mechanical systems, systems of chemical reactants, of animal populations, wave phenomena, and many more. This course discusses analytical techniques for finding solutions and for understanding their behaviour. Topics include linear differential equations as well as methods for nonlinear differential equations including an introduction to chaotic systems. Aspects of the general theory of differential equations will be discussed, the emphasis, however, will be on practical methods rather than mathematical rigour.
Aims
The aim of this unit is to introduce the students to the basic theory of ordinary differential equations and give a competence in solving ordinary differential equations by using analytical or numerical methods.
Syllabus
Here is a brief syllabus of the course:
There may be minor changes to this syllabus, or to the order of presentation.
Relation to Other Units
This unit develops the ordinary differential equations material in Core Mathematics. Partial differential equations are treated in a separate unit, Applied Differential Equations 2. Together with Calculus 2, these courses provide essential tools for mathematical methods and applied mathematics units at Levels 3 and 4. Calculus 2 is recommended but not required as a corequisite.
Transferable Skills:
The final mark for Ordinary Differential Equations is calculated as follows:
More information is given below.
Summer Examination
The examination in May/June consists of a 2 ½-hour paper consisting of FIVE questions; you should attempt FOUR. If you attempt more than four, your best four answers will be used for assessment. Calculators may NOT be used.
The final mark for Ordinary Differential Equations is calculated as follows:
More information is given below.
Summer Examination
The examination in May/June consists of a 2 ½-hour paper consisting of FIVE questions; you should attempt FOUR. If you attempt more than four, your best four answers will be used for assessment. Calculators may NOT be used.
This year, the preferred text for the course is:
Differential Equations: An Applied Approach, by J. M. Cushing, Pearson (Prentice Hall) 1 st ed. (2004)
The course syllabus includes (but not restricted to): Chapters 1, 2, 3, 4, 5, 6, section 7.3 and Chapter 8. There will be some additional material given in lectures and handouts.
You may also use the following text:
Elementary Differential Equations and Boundary Value Problems, by William E. Boyce, Richard C. Diprima, John Wiley & Sons, 8 th ed. (2005),
however some topics are not covered here. Additional literature will be given during the lectures.