Registry

Module Specifications

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

Module Title	Introduction to Numerical Methods
Module Code	MS230
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Olaf Menkens Semester 2: Olaf Menkens Autumn: Olaf Menkens
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This course introduces students to the core components of numerical analysis, with the emphasis placed on using the methods, rather than their analysis. More specifically, this know-how and skills module introduces numerical methods how to solve linear systems of algebraic equations, to find roots of non-linear equations, to integrate functions, and to solve initial and boundary value problems for ordinary differential equations.Students will participate in the following learning activities:Lectures: Students will attend a series of lectures designed to introduce learners to the mathematical principles and techniques that underpin this module.Tutorials: A series of exercise sheets will be given the class which will be discussed and solved in the tutorials.Reading: Students are expected to fully utilise the textbooks and other resources listed below.

Learning Outcomes

1. Employ various numerical methods to find roots, solve systems of equations, integrate, solve ordinary differential equations.
2. Judge what is likely to be the best method for a given problem.
3. Evaluate if the obtained answer is likely to be correct or not.

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	24	No Description
Tutorial	12	No Description
Independent learning	89	No Description
Total Workload: 125

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

Linear systems of algebraic equations.
Gaussian elimination, (scaled) partial pivoting, LU decompositon, Iterative methods..

Finding roots of nonlinear equations.
Bisection method, secant method, Newton's method, fixed point iteration..

Integration.
Rectangle rule, mid-point rule, trapezoidal rule, Simpson's rule..

Ordinary Differential Equations.
Euler's method, modified Euler's method, Runge-Kutta methods, Systems of first order ordinary differential equations (ODE's), shooting method, finite difference method..

Assessment Breakdown
Continuous Assessment	%	Examination Weight	100%

Course Work Breakdown
Type	Description	% of total	Assessment Date

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

William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery: 2007, Numerical Recipes : the Art of Scientific Computing, 3rd, Cambridge University Press, Cambridge,
Brian Bradie: 2008, A Friendly Introduction to Numerical Analysis, 1st, Pearson Prentice Hall, Upper Saddle River,
Laurene V. Fausett: 2008, Applied Numerical Analysis Using Matlab, 2nd, Pearson Prentice Hall, Upper Saddle River,
Endre Suli, David Mayers: 2008, An Introduction to Numerical Analysis, 4th, Cambridge University Press, Cambridge,
Richard L. Burden, J. Douglas Faires: 2004, Numerical Analysis, 8th, Brooks/Cole, Boston,
John H. Mathews, Kurtis D. Fink: 2005, Numerical Methods Using Matlab, 4th, Pearson Prentice Hall, Upper Saddle River,
Rainer Kress: 1998, Numerical Analysis, Springer, New York,

Other Resources

None

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