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# Module Code - Title:

MS4014 - INTRODUCTION TO NUMERICAL ANALYSIS

2022/3

2

1

1

0

6

6

N

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.

None

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# 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

Autumn - 08/09