Differential Equations

Module Identifier: MA11210
Module Title: Differential Equations
Academic Year: 2027/2028
Semester: Semester 2
Co-ordinator: Dr Adam Vellender
Reading List: View on Aspire
Pre-Requisite: MA10510 or MT10510
Pre-Requisite: MP10610
Exclusive (Any Acad Year): MT11210
Other Staff: Dr Gwion Evans

Assessment

Assessment Type	Assessment details	Proportion
Semester Assessment	Coursework: Mark based on engagement, participation and submitted assignments	20%
Semester Exam	Exam: 2 Hours (Written Examination)	80%
Supplementary Assessment	Blackboard Test:	20%
Supplementary Exam	Supplementary Exam: 2 Hours (Written Examination)	80%

Learning Outcomes

On successful completion of this module students 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
Adaptability and resilience	Completion of tasks (assignments) to set deadlines will aid personal development.
Creative Problem Solving	The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills.
Digital capability	Use of Blackboard and internet resources.
Professional communication	Written answers to exercises must be clear and well structured.
Subject Specific Skills	Broadens exposure of students to topics in mathematics.

Notes

This module is at CQFW Level 4