2008/09 Undergraduate Module Catalogue

MATH1970 Differential Equations

10 creditsClass Size: 200

Module manager: Professor A.V. Mikhailov
Email: sashamik@maths.leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2008/09

Pre-requisites

MATH1960

Calculus

This module is mutually exclusive with

MATH1400	Modelling with Differential Equations
MATH1460	Mathematics for Geophysical Sciences 1
MATH1932	Calculus, ODEs and Several-Variable Calculus

This module is approved as an Elective

Module summary

Differential equations provide a powerful mathematical method for modelling physical, chemical and biological phenomena. This introduction to the theory of differential equations cover basic methods for solving ordinary differential equations, that is, equations in which the functions depend on a single variable.

Objectives

On completion of this module, students should be able to:

a) Solve a variety of first-and second-order differential equations;
b) Derive and solve ODEs arising from applications..

Syllabus

1. Introduction. Basic definitions, examples. Geometrical interpretation. Graphical and numerical solutions.
2. First order ordinary differential equations: Linear equations, separable equations. Homogeneous equations, Bernoulli equation. Change of variables. Exact equations.
3. Second order linear ordinary differential equations. Equations with constant coefficients. equations with non-constant coefficients. Homogeneous equations: principle of superposition, solution space, basis, Wronskians, Abel¿s identity. Method of reduction of order. Inhomogeneous equations, methods of undetermined coefficients, variation of parameters.
4. Systems of linear ordinary differential equations: Homogeneous solutions. Fundamental solution matrix. Wronskians. Inhomogeneous systems. Variation of parameters.
5. Phase plane methods: Introduction. Critical points. Stability. Matrix exponential.

Teaching methods

Delivery type	Number	Length hours	Student hours
Lecture	21	1.00	21.00
Tutorial	11	1.00	11.00
Private study hours			68.00
Total Contact hours			32.00
Total hours (100hr per 10 credits)			100.00

Opportunities for Formative Feedback

Regular example sheets.

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	.	15.00
Total percentage (Assessment Coursework)		15.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 00 mins	80.00
Standard exam (closed essays, MCQs etc)	0 hr 00 mins	5.00
Total percentage (Assessment Exams)		85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 31/03/2009

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