Module Title 
Numerical Methods

Module Code 
MS213

School 
School of Mathematical Sciences

Online Module Resources

Module Coordinator  Prof John Carroll  Office Number  X139 
Level 
2

Credit Rating 
7.5

Prerequisite 
None

Corequisite 
None


Module Aims

² To introduce mathematics students to some core numerical analysis topics.
² To communicate some of the issues which arise in seeking numerical solutions to
analytic problems.
² To use C++ codes to implement some of the numerical algorithms discussed in lec
tures.
² To apply some of the numerical algorithms to practical problems.

Learning Outcomes

² An intuitive and working understanding of some numerical methods for some selected
problems of numerical analysis.
² Some appreciation of the concept of error and the need to analyze and predict it.
² Experience in the implementation of numerical methods.

Indicative Time Allowances


Hours

Lectures 
36

Tutorials 
11

Laboratories 
8

Seminars 

Independent Learning Time 
57.5



Total 
112.5

Placements 

Assignments 


NOTE

Assume that a 7.5 credit module load represents approximately 112.5 hours' work, which includes all teaching, incourse assignments, laboratory work or other specialised training and an estimated private learning time associated with the module.

Indicative Syllabus

Indicative Syllabus: Indicative Lecture hours given in below:
< 3 > Taylor Polynomials, Error and Computer Arithmetic: The Taylor polynomial, its error
and evaluation. Floating point number system. Errors. Numerical cancellation. Propagation
of error.
< 6 > Numerical Solution of a Single Nonlinear Equation: Bisection method. Newton''''s
method. Secant method. Fixedpoint iteration and acceleration techniques.
< 6 > Numerical Solution of Linear Equations I: Systems of linear equations. Matrix arith
metic. Direct methods for linear systems: Gaussian elimination with pivoting strategies,
LUdecomposition.
< 6 > Numerical Solution of Linear Equations II: Iterative methods including GaussSeidel,
Jacobi and SOR methods; Convergence criteria.
< 4 > Numerical Di®erentiation: Calculus of ¯nite di®erences. Local truncation error, rounding
error and optimal stepsizes. Method of undetermined coe±cients, Richardson extrapolation.
< 5 > Interpolation: Polynomial Interpolation. Divided di®erences and Newton''''s interpolation
formula. Equally spaced points. Interpolation errors.
< 6 > Numerical Integration: NewtonCotes formulae: Trapezoidal Rule, Simpson''''s Rule; Com
posite integration; estimating errors; Romberg integration; Gaussian quadrature.

Assessment  Continuous Assessment  25%  Examination Weight  75% 

Indicative Reading List

² K Atkinson & W Han, Elementary Numerical Analysis, 3rd Edition, John Wiley &
Sons, Inc. 2004.
² R L Burden & J D Faires, Numerical Analysis 7th edition, Brooks/Cole, 2001.
² W Cheney & D Kincaid, Numerical Mathematics and Computing, 4th edition,
Brooks/Cole, 1999.


Programme or List of Programmes

ACM  BSc Actuarial Mathematics 
BQF  BSc in Quantitative Finance 
CAFM  Common Entry into Mathematical Sciences 
Archives:  