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Module Specifications

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

Module Title Numerical Methods
Module Code MS213A
School School of Mathematics
Online Module Resources

Module TeacherJurgen Burzlaff
NFQ level 8 Credit Rating 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.



Workload Full-time hours per semester
Type Hours Description
Total Workload: 0

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
Numerical Solution of a Single Non-linear Equation.
Bisection method. Newton's method. Secant method.Fixed-point iteration and acceleration techniques..

Numerical Solution of Linear Equations (Direct Methods).
Systems of linear equations. Matrix arithmetic. Direct methods for linear systems: Gaussian elimination with pivoting strategies, LU-decomposition..

Numerical Solution of 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 Assessment0% Examination Weight100%
Course Work Breakdown
TypeDescription% of totalAssessment 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
  • R L Burden, J D Faires: 2004, Numerical Analysis, 8th, Brooks Cole, 978-0534404994
Other Resources
195, Website, John Carroll, 0, Complete Lecture Notes, www.dcu.ie/~carrollj/ms213.html, 196, Website, John Carroll, 0, Tutorial Sheets/Exam Papers, www.dcu.ie/~carrollj/ms213.html,
Array
Programme or List of Programmes
FMBSc in Financial & Actuarial Mathematics
Timetable this semester: Timetable for MS213A
Date of Last Revision15-FEB-11
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