Module Identifier MA11210  
Module Title DIFFERENTIAL EQUATIONS  
Academic Year 2007/2008  
Co-ordinator Dr David M Binding  
Semester Semester 2  
Other staff Gareth D E Lanagan, Ms Brenda M Hughes, Dr David M Binding  
Pre-Requisite MA10020  
Course delivery Lecture   22 Hours. (22 x 1 hour lectures)  
  Seminars / Tutorials   5 Hours. (5 x 1 hour tutorials)  
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours (written examination)  100%
Supplementary Assessment2 Hours (written examination)  100%

Learning outcomes

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

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
** General Text
Salas, Hille and Ergen (2003) Calculus 9th ed. Wiley 0471383759
** Recommended Text
A Jeffrey, (1992) Essentials of Engineering Mathematics Chapman and Hall 0412396807
W E Boyce & R C De Prima (2001) Elementary Differential Equations 7th. Wiley 0471089532
** Supplementary Text
Weir, M D, Haas, J and Giordano, F R (2005) Thomas' Calculus 11/e. Addison-Wesley 0321243358

Notes

This module is at CQFW Level 4