Module: Numerical Methods

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Numerical Methods
Module Code	MTH1037 (ITS: MS213)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	7.5

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

Section Breakdown
CRN	21277	Part of Term	Semester 2
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC1	Best Mark	N
Module Co-ordinator	Turlough Downes	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
Oral Examination	C++ Computing Assignments	25%	Week 11
Formal Examination	End-of-Semester Final Examination	75%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

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.

Indicative Reading List

Books:

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

Articles:
None

Other Resources

None