Gwybodaeth Modiwlau

Module Identifier
MA11210
Module Title
Differential Equations
Academic Year
2014/2015
Co-ordinator
Semester
Semester 2
Pre-Requisite
Other Staff

Course Delivery

Delivery Type Delivery length / details
Lecture 22 Hours. (22 x 1 hour lectures)
Seminars / Tutorials 5 Hours. (5 x 1 hour tutorials)

Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   (written examination)  80%
Semester Assessment Mark based on attendance at lectures and tutorials and work handed in  20%
Supplementary Exam 2 Hours   (written examination)  100%

Learning Outcomes

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

• solve elementary examples of first-order and linear second-order differential equations with given initial or boundary conditions ;
• construct simple mathematical models.

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 and physics.

Aims

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

Content

1. 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. Discussion of existence and uniqueness.
2. 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, including:
- elementary dynamics using Newton's laws of motion;
- population dynamics;
- flow of charge around simple electric circuits.

Reading List

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

Notes

This module is at CQFW Level 4