Module Information
Module Identifier
MA11210
Module Title
DIFFERENTIAL EQUATIONS
Academic Year
2011/2012
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 Assessment | 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.
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 TextSalas, 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