Module: Numerical Methods

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Numerical Methods
Module Code	MS213 (ITS) / MTH1037 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	-
Module Teachers	-
NFQ level	8	Credit Rating	7.5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

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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.

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

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	36	Presentation of Course Material
Tutorial	10	No Description
Independent Study	79	No Description
Tutorial	1	Working from supplied tutorial sheets
Laboratory	1	C++ Assignments
Lecture	3	Numerical Methods
Total Workload: 130

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

Single Non-linear Equation
Bisection 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 Differentiation
Calculus of finite differences. Local truncation error, rounding error and optimal step-sizes. Method of undetermined coefficients, Richardson extrapolation.

Interpolation
Polynomial Interpolation. Divided differences and Newton's interpolation formula. Equally spaced points. Interpolation errors.

Numerical Integration
Newton-Cotes formulae: Trapezoidal Rule, Simpson's Rule; Composite integration; estimating errors; Romberg integration; Gaussian quadrature.

Assessment Breakdown
Continuous Assessment	25%	Examination Weight	75%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Oral Examination	C++ Computing Assignments	25%	Week 11

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

R L Burden & J D Faires: 2004, Numerical Analysis, 8th, Brooks Cole, 978-0534404994
W Cheney & D Kincaid: 2003, Numerical Mathematics and Computing, 5th, Brooks Cole, 978-0534389932
W T Vetterling, W H Press, S A Teukolsky, B P Flannery: 1992, Numerical Recipes Example Book (C), 2nd, Cambridge University Press, 978-0521437202

Other Resources

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