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. |
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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 |
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LECTURER/S | Anton Buhagiar |
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The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2023/4. It may be subject to change in subsequent years. |