Registry
Module Specifications
Archived Version 2021 - 2022
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Description MS213 aims to introduce mathematics students to some core numerical methods, to enable them to understand the concept of error, and to communicate some of the issues which arise in seeking numerical solutions to analytic problems. Students will have the opportunity to apply some of the numerical algorithms to practical problems and will be required to use and modify supplied C++ codes to implement some of the numerical algorithms discussed in the lectures. | |||||||||||||||||||||||||||||||||||||||||
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Learning Outcomes 1. Apply and interpret the results of numerical methods when employed to solve problems from selected application areas of numerical analysis. 2. Construct error equations and calculate key measurements, such as optimum stepsizes, related to a given numerical method. 3. Formulate a numerical method in algorithmic form. 4. Apply and combine existing C++ codes to obtain numerical solutions to selected mathematical problems | |||||||||||||||||||||||||||||||||||||||||
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 Single Non-linear EquationBisection method. Newton's method. Secant method. Fixed-point iteration and acceleration techniques.Linear Equations (Direct Methods)Systems of linear equations. Matrix arithmetic. Direct methods for linear systems: Gaussian elimination with pivoting strategies, LU-decomposition.Linear Equations (Iterative Methods)Iterative methods including Gauss-Seidel, Jacobi and SOR methods. Convergence criteria.Numerical DifferentiationCalculus of finite differences. Local truncation error, rounding error and optimal step-sizes. Method of undetermined coefficients, Richardson extrapolation.InterpolationPolynomial Interpolation. Divided differences and Newton's interpolation formula. Equally spaced points. Interpolation errors.Numerical IntegrationNewton-Cotes formulae: Trapezoidal Rule, Simpson's Rule; Composite integration; estimating errors; Romberg integration; Gaussian quadrature. | |||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources None | |||||||||||||||||||||||||||||||||||||||||
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