Module Specifications..
Current Academic Year 2023 - 2024
Please note that this information is subject to change.
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Coursework Only Reassessment of continuous assessment will consist of one or more resit tests. |
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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 | |||||||||||||||||||||||||||||||||||||||
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 |
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Indicative Content and Learning Activities
Basic principlesComputational cost – round-off and systematic errors – estimating accuracy – order of errors – minimizing round-off errors – numerical instabilityLinear systems: Direct MethodsGaussian 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 ExcelLinear systems: Iterative methodsJacobi and Gauss-Seidel methods – convergence criteria - use of built-in iterative solver in Excel - use of Excel Solver for solving equationsRoot-findingBisection and Newton Raphson Methods - use of Goal Seek in ExcelOptimisationGolden section search – Newton s Method - steepest descent method - use of Excel Solver for single- and multi-variate optimisationNumerical integrationTrapezoidal and Simpson s Rule – Romberg integrationLinear regressionUse of Excel for best-fit linesExplicit solution of ODEsEuler 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 problemsNumerical differentiationTaylor Series and finite difference approximations - orderFinite-difference method for ODEsIntroduction to FD methodSolution of PDEs using the finite difference methodImplicit and explicit schemesIssues arising with measured and sampled dataDifferentiating and integrating measured data with noise – smoothing using moving average - aliasingCoding of numerical methodsUse of Excel and VBA for implementing numerical methods and viewing resultsData presentation and analysisPlotting 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 | |||||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources 39896, Website, 0, MM281 Loop page, | |||||||||||||||||||||||||||||||||||||||
Programme or List of Programmes
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Date of Last Revision | 17-SEP-07 | ||||||||||||||||||||||||||||||||||||||
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