Module: Engineering Computation

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Engineering Computation
Module Code	MM281 (ITS) / MEC1011 (Banner)
Faculty	Engineering & Computing	School	Mechanical & Manufacturing Eng
Module Co-ordinator	Alan Kennedy
Module Teachers	-
NFQ level	8	Credit Rating	5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Coursework Only
Reassessment of continuous assessment will consist of one or more resit tests.

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

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	20	No Description
Laboratory	36	Computer and tutorial session plus tests
Independent Study	68	Preparation for tests
Total Workload: 124

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

Linear regression
Use of Excel for 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	100%	Examination Weight	0%

Type	Description	% of total	Assessment Date
Course Work Breakdown
In Class Test	Three Excel/VBA/written tests	100%	Other

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 1

Indicative Reading List

Chapra, S., Canale, R.: 2016, Numerical Methods for Engineers, McGraw-Hill, 978-007339792

Other Resources

39896, Website, 0, MM281 Loop page,