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Department of Mathematics



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MA2021 Differential Equations and Dynamics

MA2021 Differential Equations and Dynamics

Credits: 20 Convenor: Dr. M. Dampier Semester: 1 (weeks 1 to 12)
Prerequisites: essential: MA1001, MA1002 desirable: MA1051
Assessment: Weekly exercises and computer practical: 40% 3 hour exam: 60%
Lectures: 33 Problem Classes: 10
Tutorials: none Private Study: 85
Labs: 11 Seminars: none
Project: none Other: none
Surgeries: 11 Total: 150

Subject Knowledge

Aims

This module aims to introduce the student to fundamental methods in applied mathematics, in particular the use of differential equations and their applications in dynamics. The student will also gain some experience in using the computer to solve mathematical problems.

Learning Outcomes

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.

To know how classical mechanics produces differential equations of motion both by elementary methods and by the methods of analytical dynamics, and to be able to solve a selection of important problems in dynamics using simple qualitative methods, analytical methods, and basic numerical methods using a computer package.

Methods

Lectures, computer classes, problem classes.

Assessment

Marked problem sheets, computer practical portfolio, examination.

Subject Skills

Aims

To develop students' mathematical problem solving skills, and their skills in communicating mathematical arguments, and to provide them with some basic computational skills.

Learning Outcomes

Students will have used a computer to solve some simple mathematical problems, and recorded their findings in a portfolio. Students will have improved their ability to solve problems both using pencil and paper and a computer, and will have improved their ability to write mathematical arguments.

Methods

Lectures, computer classes, problem classes.

Assessment

Marked problem sheets, marked computer practical portfolio.

Explanation of Pre-requisites

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.

Course Description

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.

Syllabus

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. Lagrange's equations - small oscillations. Orbits and numerical prediction. Hamiltonian systems.

Reading list

Recommended:

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.

Resources

Problem sheets, computer rooms, lecture rooms.

Module Evaluation

Module questionnaires, module review, year review.

Next: MA2051 Fluids and Waves Up: ModuleGuide03-04 Previous: MA2011 Differential Equations

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Last updated: 2004-02-21
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