Registry

Module Specifications

Archived Version 2017 - 2018

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 Excel and VBA 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 Excel and VBA.
5. Specify the numerical information required to solve a variety of mathematical problems.
6. Use Excel and VBA for professional data presentation and analysis

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	24	No Description
Tutorial	12	No Description
Laboratory	24	Computer session
Independent Study	14	Work on tutorial questions
Independent Study	24	Preparation for Excel/VBA 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 errors and iterative improvement - use of MINVERSE and MMULT for solving equations in Excel

Linear systems: Iterative methods
Jacobi and Gauss-Seidel methods – convergence criteria - use of built-in iterative solver in Excel - use of Excel Solver for solving equations

Root-finding
Bisection and Newton Raphson Methods - use of Goal Seek in Excel

Optimisation
Golden section search – Newton s Method - steepest descent method - use of Excel Solver for single- and multi-variate optimisation

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 - 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

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 Excel and VBA for implementing numerical methods and viewing results

Data presentation and analysis
Plotting data in Excel; data-fitting; using Excel for simple sensitivity analyses; data sorting and filtering; conditional formatting and data validation; use of database-related functions

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.: 2005, Numerical Methods for Engineers, 5th, McGraw-Hill,
Pozrikidis, C.: 1998, Numerical Computation in Science and Engineering, Oxford University Press,

Other Resources

22801, Website, 0, MM281 Loop page,

Programme or List of Programmes

CAM	B.Eng. Mechanical & Manufacturing Eng
ECSA	Study Abroad (Engineering & Computing)
ECSAO	Study Abroad (Engineering & Computing)

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