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Department of Mathematics



Next: MA2061 Lagrangian and Hamiltonian Dynamics Up: ModuleGuide03-04 Previous: MA2021 Differential Equations and Dynamics

MA2051 Fluids and Waves

MA2051 Fluids and Waves

Credits: 10 Convenor: Dr. M. Dampier Semester: 2 (weeks 19 to 24)
Prerequisites: essential: MA2001
Assessment: Weekly exercises and computer practical: 40% 1.5 hour exam: 60%
Lectures: 18 Problem Classes: 5
Tutorials: none Private Study: 42
Labs: 5 Seminars: none
Project: none Other: none
Surgeries: 5 Total: 75

Subject Knowledge

Aims

The module aims to provide a mathematical introduction to the mechanics of inviscid fluids, and to apply the theory to wave phenomena. Waves in other media may also be considered.

Learning Outcomes

To know how to describe fluid flow, to understand the role of contact forces, and to learn how to use the concept of pressure, to be able to use the basic equations of inviscid fluid dynamics in a variety of simple situations, to understand the basic concepts of wave motion - wave equation, frequency, wavelength.

Methods

Lectures, computer classes, problem classes.

Assessment

Marked problem sheets, computer practical portfolio, examination.

Subject Skills

Aims

To provide students with computing skills and develop written communication skills and problem solving skills.

Learning Outcomes

Students will have used a computer to solve some simple mathematical problems, and recorded their findings in a portfolio. Students will have improved their ability ot solve problems both using pencil and paper and a computer.

Methods

Lectures, computer classes, problem classes.

Assessment

Marked problem sheets, marked computer practical portfolio.

Explanation of Pre-requisites

The work on vector calculus in MA2001, will form a basis for this module. A general mathematical knowledge from other modules is also required.

Course Description

This is an essential module for those wishing to take certain later modules in Applied Mathematics, for example Fluids and Waves, General Relativity, Electromagnetic Theory etc. The course adevelops the ideas of mechanics to a continuous medium.

Syllabus

Introduction to vector algebra.

Introduction of suffix notation and the summation convention including $\delta_{ij}$ and $\epsilon_{ijk}$.

Fluids, density, velocity field, conservation of mass. Pressure, material derivative, Euler's equation. Hydrostatics, liquids and gases, atmospheric equilibrium. Steady flow, streamlines, Bernoulli's equation. Streams of constant breadth. Vorticity, irrotational motion. Compressible flow, sound waves. Other examples of wave motion.

Reading list

Recommended:

D.J.Acheson, Elementary Fluid Dynamics, Oxford. This book contains considerably more material than is covered in this module, but chapters 1 and 3 give a good coverage of most of the topics required..

Background:

Resources

Problem sheets, computer rooms, lecture rooms.

Module Evaluation

Module questionnaires, module review, year review.

Next: MA2061 Lagrangian and Hamiltonian Dynamics Up: ModuleGuide03-04 Previous: MA2021 Differential Equations and Dynamics

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Last updated: 2004-02-21
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