Latest Module Specifications
Current Academic Year 2025 - 2026
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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. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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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 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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List Books:
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Other Resources
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