School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2020/21 Last Updated: 30 May 2020

MAT-30011 - Waves

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MAT-20004 Complex Variable I and Vector Calculus

MAT-20008 Differential Equations

MAT-20008 Differential Equations

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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 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.

demonstrate knowledge of the theory of the wave equation;: 1,2,

solve the wave equation by separation of variables;: 1,2,

demonstrate knowledge of the theory of waves on stretched strings;: 1,2,

demonstrate knowledge of the theory of waves on stretched membranes;: 1,2,

demonstrate knowledge of the theory of bending waves on beams;: 1,2,

solve the governing equation for bending waves on beams by Fourier and Laplace Transforms;: 1,2,

demonstrate knowledge of the theory of sound waves;: 1,2,

demonstrate knowledge of the theory of waves in liquids with a free surface;: 1,2,

solve the governing equations for waves in liquids.: 1,2,

solve the wave equation by separation of variables;: 1,2,

demonstrate knowledge of the theory of waves on stretched strings;: 1,2,

demonstrate knowledge of the theory of waves on stretched membranes;: 1,2,

demonstrate knowledge of the theory of bending waves on beams;: 1,2,

solve the governing equation for bending waves on beams by Fourier and Laplace Transforms;: 1,2,

demonstrate knowledge of the theory of sound waves;: 1,2,

demonstrate knowledge of the theory of waves in liquids with a free surface;: 1,2,

solve the governing equations for waves in liquids.: 1,2,

Lectures: 25 hours

Examples Classes: 5 hours

Preparation of coursework: 30 hours

Independent study: 88 hours

Unseen examination : 2 hours

Examples Classes: 5 hours

Preparation of coursework: 30 hours

Independent study: 88 hours

Unseen examination : 2 hours

None

Approximately 4 assignments set at regular intervals

Continuous assessment will consist of written coursework, problem sheets, class tests, or any combination thereof.

2 HOUR UNSEEN EXAM

The examination paper will consist of no less than five and not more than eight questions all of which are compulsory.