MA11210 - DIFFERENTIAL EQUATIONS

Module Identifier	MA11210
Module Title	DIFFERENTIAL EQUATIONS
Academic Year	2002/2003
Co-ordinator	Rowland S Jones
Semester	Semester 2
Pre-Requisite	MA10020
Course delivery	Lecture	20 x 1 hour lectures
	Seminars / Tutorials	5 x 1 hour tutorials
	Other	Workshop. 2 x 1 hour workshops (including test)
Assessment	Semester Exam	2 Hours (written examination)	75%
	Semester Assessment	Continuous Assessment:	25%
	Supplementary Assessment	2 Hours (written examination)	100%

Learning outcomes

On completion of this module, a student should be able to:

construct a simple mathematical model;
solve first-order and linear second-order differential equations with given initial or boundary conditions.

Brief description

Mathematics is perhaps the most efficient and successful way of describing the real world. The purpose of this module is to introduce students to the notion of mathematical modelling and to develop the technical skills for the solution of the mathematical problems that arise in applications. The syllabus will include techniques of integration, first-order and linear second-order differential equations. Examples will be taken from biology, economics anad physics.

Aims

To develop technical skills and a facility for using calculus in applications.

Content

1. MATHEMATICAL MODELLING: The use of mathematical models to describe and understand the real world. Differentiation and rates of change. Formulation of differential equations to describe time-dependent phenomena. Elementary kinematics. Newton's laws of motion. Population dynamics and related problems.
2. DIFFERENTIAL EQUATIONS: First-order equations with separable variables. Homogeneous and linear first-order equations. Linear second-order equations with constant coefficients. Determination of particular integrals when the non-homogeneous term is a polynomial, circular function or exponential function. Method of variation of parameters. Initial and boundary value problems. Higher order linear equations with constant coefficients. Examples from biology, economics and physics. Discussion of existence and uniqueness.

Reading Lists

Books
** Recommended Text
W E Boyce & R C De Prima. (2001) Elementary Differential Equations. 7th. Wiley 0471089532
A Jeffrey, [J]. (1992) Essentials of Engineering Mathematics. Chapman and Hall 0412396807