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2010/1 Module Catalogue
 Module Code: ENG2001 Module Title: MATHEMATICS 2A
Module Provider: Mechanical, Medical & Aero Engineering Short Name: SE0201
Level: HE2 Module Co-ordinator: ROCKLIFF NJ Dr (M, M & A Eng)
Number of credits: 10 Number of ECTS credits: 5
 
Module Availability
Autumn Semester
Assessment Pattern

Unit(s) of Assessment
Weighting Towards Module Mark (%)
Written examination
80
Tutorial tests
20
Qualifying Condition(s) 
A weighted aggregate mark of 40% is required to pass the module

Module Overview

Engineers need to develop a range of mathematical techniques for the solution of engineering problems, many of which are modeled by ordinary or partial differential equations. However in addition to having the ‘toolkit’ of techniques engineers also need to be able to select the appropriate method for the problem and be able to relate their solution to the physical result. This module introduces a number of new concepts and methods and looks at their application to simplified but realistic engineering models. 

Prerequisites/Co-requisites

Completion of the progress requirements of Level HE1 and Modules ENG1001 (or ENG1011) and ENG1002
Module Aims

The aims of the module are:

 

·                   To extend students' knowledge and understanding of previously encountered mathematical

 

           concepts and techniques

 

·                   To introduce new mathematical tools and techniques

 

·                   To develop an understanding of the applicability of the methods

 

·                   To interpret the mathematical solutions in physical terms

 

  • To enable them to solve more complex engineering problems.
Learning Outcomes
 

On successful completion of the module you should be able to

 

  • apply  Laplace transform (and inverse LT) definitions and properties to mathematical expressions

     

  • use transform methods for the analysis of initial value problems

     

  • solve basic matrix eigenvalue roblems

     

  • formulate suitable differential equation sets as eigenvalue problems and hence solve the differential equations

     

  • interpret solutions of these eigenvalue problems in physical context (e.g. normal modes of vibration)

     

  • decompose periodic signals into sinusoidal components and interpret the result

     

  • solve differential equations in several variables. 

     

  • select appropriate mathematical methods for the analysis of engineering problems or data
Module Content

Laplace transforms (8 hours):
Definition and standard forms, operational properties, unit step and Dirac delta functions.

 

Solution of ODEs and systems of ODEs with initial conditions.

Further matrix algebra (6 hours):
Revision of matrices and determinants. Eigenvalues and eigenvectors, applications to systems of linear differential equations and normal modes.

 


Fourier series (5 hours):
Periodic and trigonometric series, Fourier series for functions of any period, odd and even functions, half range Fourier series; applications.

Partial differential equations (5 hours):
Introduction to PDE's, solution of 2nd order linear PDS using trial solutions, full separation of variables method

 

 
Methods of Teaching/Learning

24 hours of lectures, 12 hours of tutorial classes, including 4 20-minute open-book tutorial tests, 64 hours independent learning and 2 hour exam

Total student learning time 100 hours
Selected Texts/Journals

Required reading

 

Kreyszig E, WIE Advanced Engineering Mathematics, 9th edition (or earlier), Wiley, 2006. (ISBN 978-0-471-72897-9)
James G, Advanced Modern Engineering Mathematics, 3rd edition (or earlier), Pearson Prentice Hall, 2003. (ISBN13 9780130454256, ISBN10: 0130454257)

 

 
Last Updated

12 October 2009