|
Module Title |
Numerical Methods
|
|
Module Code |
MS213
|
|
School |
School of Mathematical Sciences
|
Online Module Resources
|
| Module Co-ordinator | Prof John Carroll | Office Number | X139 |
|
Level |
2
|
Credit Rating |
7.5
|
|
Pre-requisite |
None
|
|
Co-requisite |
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, in-course 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 Non-linear Equation: Bisection method. Newton''''s
method. Secant method. Fixed-point 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,
LU-decomposition.
< 6 > Numerical Solution of Linear Equations II: Iterative methods including Gauss-Seidel,
Jacobi and SOR methods; Convergence criteria.
< 4 > Numerical Di®erentiation: Calculus of ¯nite di®erences. Local truncation error, rounding
error and optimal step-sizes. 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: Newton-Cotes 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: | |
