Module Code - Title:

MS4014 - INTRODUCTION TO NUMERICAL ANALYSIS

Year Last Offered:

2023/4

Hours Per Week:

Lecture

2

Lab

1

Tutorial

1

Other

0

Private

6

Credits

6

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, NewtonÆs method, Secant method, fixed point method; convergence criteria, rate of convergence, effect of multiplicity of zero; introduction to the use of NewtonÆs method for systems of nonlinear equations. Systems of linear equations: Gauss elimination, LU and Cholesky factorisation, ill-conditioning, condition number; iterative methods: Jacobi, Gauss-Seidel, SOR, convergence criterion. Interpolation and Quadrature: Lagrange interpolation, error formula; Newton-Cotes 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 ill-conditioned 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