Registry

Module Specifications

Archived Version 2012 - 2013

Module Title	Engineering Computation
Module Code	MM281
School	School of Mechanical and Manufacturing Engineering
Online Module Resources
Module Co-ordinator	Dr Alan Kennedy	Office Number	S367
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This module aims to introduce concepts in numerical methods and to enable the students to use Matlab and Excel to solve engineering problems using numerical schemes.

Learning Outcomes

1. Explain the purpose and limitations of numerical methods.
2. Describe and explain the implementation of a range of numerical methods.
3. Implement these methods on paper.
4. Implement these methods using a suitable programming language (e.g. Matlab) and using Excel.
5. Specify the numerical information required to solve a variety of mathematical problems.

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	24	No Description
Tutorial	12	No Description
Lecture	24	Computer session
Independent Study	14	Work on tutorial questions
Independent Study	24	Preparation for Matlab tests
Independent Study	27	Preparation for exam
Total Workload: 125

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

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

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

Linear systems: 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 - splines

Linear regression
Derivation of equations for least-squares best-fit lines

Explicit 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) - Shooting method for boundary value problems

Numerical differentiation
Taylor Series and finite difference approximations - order

Finite-difference method for ODEs
Introduction to FD method

Solution of PDEs using the finite difference method
Implicit and explicit schemes

Modal analysis
Analysis of vibrating string using finite difference method

Issues arising with measured and sampled data
Differentiating and integrating measured data with noise – smoothing using moving average - aliasing

Coding of numerical methods
Use of Matlab and Excel for implementing numerical methods and viewing results

Assessment Breakdown
Continuous Assessment	50%	Examination Weight	50%

Type	Description	% of total	Assessment Date
Course Work Breakdown

Reassessment Requirement
Resit arrangements are explained by the following categories; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
Unavailable

Indicative Reading List

Chapra, S., Canale, R.: 1998, Numerical Methods for Engineers, 3rd, McGraw-Hill,
Pozrikidis, C.: 1998, Numerical Computation in Science and Engineering, Oxford University Press,
Hahn, B.D., Valentine, D.T.: 2007, Essential Matlab for Engineers and Scientists, 3rd, Butterworth Heinemann,

Other Resources

0, Website, 0, MM281 Website, http://webpages.dcu.ie/~kennedal,

Programme or List of Programmes

BSSA	Study Abroad (DCU Business School)
BSSAO	Study Abroad (DCU Business School)
CAM	B.Eng. Mechanical & Manufacturing Eng
ECSA	Study Abroad (Engineering & Computing)
ECSAO	Study Abroad (Engineering & Computing)
HMSA	Study Abroad (Humanities & Soc Science)
HMSAO	Study Abroad (Humanities & Soc Science)
SHSA	Study Abroad (Science & Health)
SHSAO	Study Abroad (Science & Health)

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