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Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Numerical Methods
Module Code MS213
School School of Mathematical Sciences
Module Co-ordinatorSemester 1: Turlough Downes
Semester 2: Turlough Downes
Autumn: Turlough Downes
Module TeachersTurlough Downes
Martin Friesen
NFQ level 8 Credit Rating 7.5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None

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

Workload Full-time hours per semester
Type Hours Description
Lecture36Presentation of Course Material
Tutorial10No Description
Independent Study79No Description
Tutorial1Working from supplied tutorial sheets
Laboratory1C++ Assignments
Lecture3Numerical 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.

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 Assessment25% Examination Weight75%
Course Work Breakdown
TypeDescription% of totalAssessment Date
Oral ExaminationC++ Computing Assignments25%Week 11
Reassessment Requirement Type
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
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

Programme or List of Programmes
ACMBSc in Actuarial Mathematics
AFUAge Friendly University Programme
BSSAStudy Abroad (DCU Business School)
BSSAOStudy Abroad (DCU Business School)
CAFMCommon Entry, Actuarial, Financial Maths
HMSAStudy Abroad (Humanities & Soc Science)
HMSAOStudy Abroad (Humanities & Soc Science)
IESAStudy Abroad (Institute of Education)
IESAOStudy Abroad (Institute of Education)
SHSAStudy Abroad (Science & Health)
SHSAOStudy Abroad (Science & Health)
Date of Last Revision15-FEB-11

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