Module Identifier MA11210 Module Title DIFFERENTIAL EQUATIONS Academic Year 2001/2002 Co-ordinator Dr R Jones Semester Semester 2 Pre-Requisite MA10020 Course delivery Lecture 20 x 1 hour lectures Seminars / Tutorials 5 x 1 hour tutorials Workshop 2 x 1 hour workshops (including test) Assessment Continuous assessment 25% Exam 2 Hours (written examination) 75% Resit assessment 2 Hours (written examination) 100%

#### General 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.

#### 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.

#### Syllabus

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.