Registry

Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Numerical Methods
Module Code	MS213
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: John Carroll Semester 2: John Carroll Autumn: John Carroll
Module Teacher	John Carroll
NFQ level	8	Credit Rating	7.5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

MS213 aims to introduce mathematics students to some corenumerical 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*
Lecture	3	Presentation of Course Material
Tutorial	1	Working from supplied tutorial sheets
Lab	1	C++ Assignments
Lecture	3	Numerical Methods
Total Workload: 8

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 undeterminedcoefficients, 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%

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

Reassessment Requirement
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

212, Website, John Carroll, 0, MS213 Lecture Notes, www.dcu.ie/~carrollj/ms213.html, 213, Website, John Carroll, 0, MS213 Tutorial Sheets & Exam Papers, www.dcu.ie/~carrollj/ms213.html, 214, Website, John Carroll, 0, C++ Codes & Advice Note, www.dcu.ie/~carrollj/ms213.html,

Array

Programme or List of Programmes

ACM

BSc Actuarial Mathematics

CAFM

Common Entry into Mathematical Sciences

ECSAO

Study Abroad (Engineering & Computing)

SHSA

Study Abroad (Science & Health)

SHSAO

Study Abroad (Science & Health)