Module Code  Title:
MS4014

INTRODUCTION TO NUMERICAL ANALYSIS
Year Last Offered:
2022/3
Hours Per Week:
Grading Type:
N
Prerequisite Modules:
MS4022
MS4403
Rationale and Purpose of the Module:
This module provides an introduction to the basic concepts of numerical analysis.
Syllabus:
Propagation of floating point error;
Zeroes of nonlinear functions: Bisection method, NewtonÃ†s method, Secant method, fixed point method; convergence criteria, rate of convergence, effect of multiplicity of zero; introduction to the use of NewtonÃ†s method for systems of nonlinear equations.
Systems of linear equations: Gauss elimination, LU and Cholesky factorisation, illconditioning, condition number; iterative methods: Jacobi, GaussSeidel, SOR, convergence criterion.
Interpolation and Quadrature: Lagrange interpolation, error formula;
NewtonCotes and Romberg quadrature.
Numerical solution of ordinary differential equations: initial and boundary value problems, Runge Kutta and Adams Moulton methods, application to systems of ordinary differential equations.
Learning Outcomes:
Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)
On completion of this module a student should be able to:
find the real roots, and the respectove multuplicities, of a nonlinear equation
using the bisection method, Newton's method, modified Newton's methods and secant method;
find the solution of a system of linear equations using Gauss Elimination, LU factorisation or Cholesky decomposition as appropriate;
determine if a system of equations is illconditioned and determine the condition number;
determine whether the Jacobi and Gauss Seidel methods are convergent for a particular system of equations and use these methods and SOR to find the solution;
find the Lagrange interpolating polynomial for a given set of function values and estimate the error;
calculate numerical approximations to a definite integral using composite Trapezoidal and Simpson's methods, Romberg extrapolation and Guassian quadrature;
solve first ordder initial value problems using Runge Kutta and predictor corrector methods.
Affective (Attitudes and Values)
None
Psychomotor (Physical Skills)
None
How the Module will be Taught and what will be the Learning Experiences of the Students:
Research Findings Incorporated in to the Syllabus (If Relevant):
Prime Texts:
Kincaid, D. and Cheney, W, (2001)
Numerical analysis  Mathematics of Scientific Computing
, Brooks Cole
Other Relevant Texts:
Burden, R.L. and Faires, J.D. (2004)
Numerical Analysis
, Brooks Cole
Atkinson, K. ()
Elementary Numerical Analysis
, Wiley
Programme(s) in which this Module is Offered:
Semester  Year to be First Offered:
Autumn

08/09
Module Leader:
kevin.moroney@ul.ie