MATH10232 - 2006/07

Specification

Aims

The programme unit aims to discuss ordinary differential equations with applications to physical situations using Matlab to illustrate some of the ideas and methods.

Brief Description of the unit

The unit will be in 3, approximately 11 lecture sections. The first part on first order ordinary differential equations; the second part on motion in space; and the final part on second order ordinary differential equations.

Learning Outcomes

On completion of this unit successful students will be able to solve first order and second order linear problems and first order separable equations analytically. Use substitution methods and power series methods to find solutions. Be able to investigate solutions using direction fields and Euler's method. Have used Matlab as a mathematical tool and used differential equations to solve problems in mechanics and other applications.

Future topics requiring this course unit

None

Syllabus

1. Ordinary differential equations: order; linear and autonomous equations; solutions by integration; initial and boundary conditions; existence and uniqueness of solution.
2. Applications: motion in a straight line; population modelling including predator prey equations.
3. Computer methods: direction fields; Taylor series approximation; Taylor's method; Euler's method; some topics from Matlab.
4. Analytic methods for first order equations: separable equations; autonomous equations; linear equations; standard substitution methods.
5. Phase diagrams for two dimensional autonomous systems.
6. Motion in space: vector functions and space curves; arc length and curvature; velocity and acceleration; Kepler's law of planetry motion.
7. Second order equations: Linear homogeneous equations; power series; special problems {y''=f(x,y'); y''=f(y,y'); y''=y(y)}; application to springs including resonance.

Textbooks

James Stewart, Calculus, Early Transcendentals, Thomson, 5th Edition, International Student Edition, 2003.

C. H Edwards, Elementary differential equations with boundary value problems, Pearson Prentice Hall, 2004.

Teaching and learning methods

Assessment

Coursework; Weighting within unit 15%

Supervision; Weighting within unit 10%

Two hours and half end of semester examination; Weighting within unit 75%

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Arrangements