![]() | Department of Mathematics | |||
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Credits: 10 | Convenor: Dr. M. Dampier | Semester: 1 (weeks 2 to 6) |
Prerequisites: | essential: MA1001, MA1002 | |
Assessment: | Weekly exercises and computer practical: 40% | 1.5 hour exam: 60% |
Lectures: | 15 | Problem Classes: | 5 |
Tutorials: | none | Private Study: | 45 |
Labs: | 5 | Seminars: | none |
Project: | none | Other: | none |
Surgeries: | 5 | Total: | 75 |
To know and be able to use both the analytic and the geometric interpretation of differential equations. To be able to analyse linear systems of differential equations, understand the idea of a fundamental matrix, use the method of variation of parameters, and solve systems with constant coefficients in the generic case.
The work on differential equations and vectors which was covered in MA1002 will be consolidated and extended by this module. Material from MA1001 on curves and partial differentiation will also be built upon. The module MA1051 on Introductory Newtonian Dynamics will also be useful but is not an essential prerequisite. A general mathematical knowledge from other modules is also required.
This module will extend the differential equations of the first year to systems of differential equations, and apply the new ideas to important problems in classical dynamics and other areas. This is an essential module for those wishing to take certain later modules in Applied Mathematics, for example Ordinary Differential Equations.
Geometrical interpretation of first order differential equations. One dimensional motion in dynamics - the energy diagram. One dimensional motion in dynamics - phase space. Linear systems of differential equations - general theory. Linear systems of differential equations - constant coefficients.
D. K. Arrowsmith and C. M. Place, Dynamical Systems, Chapman and Hall, 1992.
N. M. J. Woodhouse, Introduction to Analytical Dynamics, Oxford University Press, 1987.
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Author: C. D. Coman, tel: +44 (0)116 252 3902
Last updated: 2004-02-21
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This document has been approved by the Head of Department.
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