Gwybodaeth Modiwlau

Module Identifier
MA11210
Module Title
Differential Equations
2021/2022
Co-ordinator
Semester
Semester 2
Pre-Requisite
Pre-Requisite
Other Staff

Assessment

Due to Covid-19 students should refer to the module Blackboard pages for assessment details

Assessment Type Assessment length / details Proportion
Semester Assessment Coursework  Mark based on attendance at lectures and tutorials and work handed in  20%
Semester Exam 2 Hours   (Written Examination)  80%
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.

Module Skills

Skills Type Skills details
Required throughout

Notes

This module is at CQFW Level 4