Study-Unit Description

Study-Unit Description


CODE MAT2913

 
TITLE Numerical Analysis

 
UM LEVEL 02 - Years 2, 3 in Modular Undergraduate Course

 
MQF LEVEL 5

 
ECTS CREDITS 2

 
DEPARTMENT Mathematics

 
DESCRIPTION - Locating roots of equations:
    - The Newton-Raphson method in one and two dimensions: rate of convergence,
    - The variable secant method,
    - The fixed point theorem for equations like x = f(x) ,
    - The method of steepest descent;

- Solution of linear equations:
    - Gaussian elimination,
    - Cholesky’s LU and LLT methods,
    - Iterative methods: Jacobi, Gauss-Seidel and the SOR methods;

- Interpolation:
    - Lagrangian interpolation,
    - The difference table and the Newton Gregory forward polynomial,
    - Inverse interpolation,
    - Spline interpolation;

- Numerical differentiation:
    - Central difference formulae for the first and second derivatives,
    - Forward difference formulae for the first derivative,
    - Improvement by extrapolation;

- Numerical integration:
    - Trapezoidal rule and Simpson’s 1/3 and 3/8 rules,
    - Errors for the local and global versions of these rules;

- Ordinary differential equations:
    - Euler’s method,
    - The modified Euler method,
    - The Runge-Kutta method;

- The finite difference method for partial differential equations:
    - Laplace’s equation,
    - Poisson’s equation.

Textbooks

- Gerald C.F. and Wheatley P.O., Applied Numerical Analysis, 6th Edition, Addison-Wesley, 1997.

Supplementary Reading

- Press W.H., Flannery B.P., et al., Numerical Recipes in Fortran, Cambridge University Press, 1989.
- Rajasekaran S., Numerical Methods in Science and Engineering, 2nd Edition, Wheeler Publishing, 1999.
- Burden R.L. and Faires J.D., Numerical Analysis, 7th Edition, Brooks Cole, London, 2001.
- Cheney E.W. and Kincaid D.R., Numerical Mathematics and Computing, 4th Edition, Brooks Cole, 1999.

 
RULES/CONDITIONS In TAKING THIS UNIT YOU CANNOT TAKE MAT2814 OR TAKE PHY2160

 
ADDITIONAL NOTES Follows from: MAT1090

 
STUDY-UNIT TYPE Lecture

 
METHOD OF ASSESSMENT
Assessment Component/s Sept. Asst Session Weighting
Examination (1 Hour and 30 Minutes) Yes 100%

 
LECTURER/S Anton Buhagiar

 

 
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