Module Catalogue 2024/25

Pre Requisite Comment

MAS1611 or MAS1607 are acceptable in place of PHY1029

Co Requisite Comment

N/A

Aims

To introduce the mathematics needed to formulate and solve problems involving ordinary and partial differential equations.

Module Summary

This module continues the exploration of differential equations that started in Stage 1, with emphasis on methods to solve them, both exact and approximate. The essential elements in the theory of ordinary and partial differential equations, and their methods of solution, introduced in this module, provide the basis for specific studies in other modules. Fourier series and transform will be introduced in this context. The methods that will be introduced, justified and practiced apply to a wide range of ordinary and partial differential equations.

Outline Of Syllabus

A review of ordinary and partial differential equations;

Series solutions of ordinary differential equations.

Fourier series and Fourier transform.

Second-order partial differential equations. Separation of variables in Cartesian coordinates: application to the wave, heat and Laplace’s equations.

Intended Knowledge Outcomes

Students will know:


the power-series representations for the solutions of ordinary differential equations;

the notion of the orthogonality of functions;

the meaning and applications of Fourier series and transform;

Laplace’s, heat and wave equations, methods of their solution in Cartesian coordinates.

Intended Skill Outcomes

Students will be able to:



construct power series solutions of ordinary differential equations;

represent a wide class of functions as Fourier series;

find separable solutions for suitable partial differential equations;

perform direct and inverse Fourier transforms of simple functions.



Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition: remember, understand, apply, analyse, evaluate and create).

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work.

Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

General Notes

N/A