MAT-30011 - Waves
Coordinator: Julius Kaplunov Tel: +44 1782 7 33526
Lecture Time: See Timetable...
Level: Level 6
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2022/23

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

MAT-20004 Complex Variable I and Vector Calculus
MAT-20008 Differential Equations

Barred Combinations

None

Description for 2022/23

The module aims to give an account of the underlying mathematical theory that describes the behaviour of waves. The mathematical development of the subject is combined with a discussion of applications, for example musical instruments. The module material is illuminated by small demonstrations and by computer-generated animations of wave processes. The topics include: the wave equation, waves on stretched strings, waves on membranes, waves on beams, sound waves, and waves in liquids with a free surface.
The module develops the following Keele Graduate attributes:
1. An open and questioning approach to ideas, demonstrating curiosity and independence of thought.
2. An appreciation of the development and value of Mathematics and the links between different areas of the subject.
4. The ability creatively to solve problems using a range of different approaches and techniques, and to determine which techniques are appropriate for the problem at hand.
6. The ability to communicate clearly and effectively in written form.

Aims
The aim of this module is to provide an account of the underlying mathematical theory that describes the behaviour of waves.

Intended Learning Outcomes

demonstrate knowledge of the theory of the wave equation: 1,3
solve the wave equation by separation of variables: 1,2,3
demonstrate knowledge of the theory of waves on stretched strings: 1,2,3
demonstrate knowledge of the theory of waves on stretched membranes: 2,3
demonstrate knowledge of the theory of bending waves on beams: 3
solve the governing equation for bending waves on beams by Fourier and Laplace Transforms: 3
demonstrate knowledge of the theory of sound waves: 3
demonstrate knowledge of the theory of waves in liquids with a free surface: 3
solve the governing equations for waves in liquids: 3

Study hours

Lectures: 25 hours
Examples Classes: 5 hours
Preparation of coursework: 30 hours
Independent study: 88 hours
Unseen examination : 2 hours

School Rules

None

Description of Module Assessment

1: Assignment weighted 15%
Assignment
Take-home assignment. Students are expected to spend 10 hours in revision and fulfilling this assignment.

2: Class Test weighted 15%
40-minute class test
A 40-minute class test will rely on the chapters for waves on strings and membranes

3: Unseen Exam weighted 70%
2-hour unseen exam
The 2 hour examination paper will consist of no less than five and not more than eight questions all of which are compulsory.