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Module Specifications

Archived Version 2009 - 2010

Module Title Engineering Computation
Module Code MM281
School School of Mechanical and Manufacturing Engineering

Online Module Resources

Module Co-ordinatorDr Alan KennedyOffice NumberS367
Level 2 Credit Rating 5
Pre-requisite None
Co-requisite None
Module Aims

The aims are to introduce concepts in numerical methods and for the students to use Matlab to solve engineering problems using numerical schemes.



Learning Outcomes

On completion of this module, the student will be able to

  • Describe a range of numerical methods, how they are implemented, why errors occur in their results, and how these errors can be minimised.
  • Demonstrate that they can use these methods to solve mathematical and engineering problems.
  • Use Matlab to implement these methods and to solve engineering problems.


Indicative Time Allowances
Hours
Lectures 24
Tutorials 11
Laboratories 24
Seminars 0
Independent Learning Time 16
Total 75
Placements
Assignments
NOTE
Assume that a 5 credit module load represents approximately 75 hours' work, which includes all teaching, in-course assignments, laboratory work or other specialised training and an estimated private learning time associated with the module.

Indicative Syllabus

·         Computational cost – round-off and systematic errors – estimating accuracy – order of errors – minimizing round-off errors – numerical instability

·         Solving sets of linear equations

·         Direct Methods: Gaussian elimination – round-off error and pivoting - Gauss-Jordan method - Thomas algorithm – condition number – residual and iterative improvement

·         Iterative methods: Jacobi and Gauss-Seidel methods – convergence criteria

·         Root-finding: Bisection and Newton Raphson Methods

·         Optimisation: – Golden section search – Newton’s Method - steepest descent method

·         Numerical integration: Trapezoidal and Simpson’s Rule – Romberg integration

·         Interpolation – polynomial fits – Vandermonde matrices

·         Linear regression

·         Solution of ODEs – Euler’s Method – first and higher order - systems of equations - Runge-Kutta methods – step-size control - interval-halving – stiff ODEs and ill-conditioned problems – stability criterion for Euler’s method (eigenvalues)

·         Boundary-Value Problems- Shooting Method

·         Numerical differentiation: Taylor Series and finite difference approximations - order

·         Finite-difference method for ODEs

·         Solution of PDEs using the finite difference method – implicit and explicit schemes

·         Modal analysis of vibrating string using finite difference method

·         Differentiating and integrating measured data with noise – smoothing using moving average

·         Aliasing

·         Use of Matlab for implementing numerical methods and viewing results

Assessment:

3 Matlab group projects - 10/3% each

2 MATLAB tests - 15% each

Written questions during tutorial sessions - 4x2.5%

Assessment
Continuous Assessment50% Examination Weight50%
Indicative Reading List

1.      Chapra, S., Canale, R., Numerical Methods for Engineers, 3rd Ed., McGraw-Hill, 1998

2.      Pozrikidis, C., Numerical Computation in Science and Engineering, Oxford University Press, 1998

3.      Hahn, B.D., Valentine, D.T., Essential Matlab for Engineers and Scientists, 3rd Ed., Butterworth-Heinemann, 2007

Programme or List of Programmes
BMEBEng Manufacturing Engineering &Business
BSSAStudy Abroad (DCU Business School)
BSSAOStudy Abroad (DCU Business School)
CAMB.Eng. Mechanical & Manufacturing Eng
ECSAStudy Abroad (Engineering & Computing)
ECSAOStudy Abroad (Engineering & Computing)
HMSAStudy Abroad (Humanities & Soc Science)
HMSAOStudy Abroad (Humanities & Soc Science)
SHSAStudy Abroad (Science & Health)
SHSAOStudy Abroad (Science & Health)
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