Programme/Approved Electives for 2022/23
Available as a Free Standing Elective
MAT-20004 Complex Variable I and Vector CalculusMAT-20008 Differential Equations
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.
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: 1,3solve the wave equation by separation of variables: 1,2,3demonstrate knowledge of the theory of waves on stretched strings: 1,2,3demonstrate knowledge of the theory of waves on stretched membranes: 2,3demonstrate knowledge of the theory of bending waves on beams: 3solve the governing equation for bending waves on beams by Fourier and Laplace Transforms: 3demonstrate knowledge of the theory of sound waves: 3demonstrate knowledge of the theory of waves in liquids with a free surface: 3solve the governing equations for waves in liquids: 3
Lectures: 25 hoursExamples Classes: 5 hoursPreparation of coursework: 30 hoursIndependent study: 88 hoursUnseen examination : 2 hours
1: Assignment weighted 15%
Description of Module Assessment
AssignmentTake-home assignment. Students are expected to spend 10 hours in revision and fulfilling this assignment.2: Class Test weighted 15%
40-minute class testA 40-minute class test will rely on the chapters for waves on strings and membranes3: Unseen Exam weighted 70%
2-hour unseen examThe 2 hour examination paper will consist of no less than five and not more than eight questions all of which are compulsory.