| CODE | MAT3806 | ||||||
| TITLE | Optimisation, Complex and Numerical Analysis 2 | ||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||
| MQF LEVEL | Not Applicable | ||||||
| ECTS CREDITS | 4 | ||||||
| DEPARTMENT | Mathematics | ||||||
| DESCRIPTION | - Functions of a complex variable: - Contour integration, - Fundamental theorem of calculus, - Cauchy’s theorem, - Cauchy’s integral formulae, - Sequences and series, - Taylor’s series, - Laurent’s series, - Zeros and poles, - Residues. - Numerical analysis: - Interpolation: - Lagrangian interpolation, - The divided difference table, - 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, - Gaussian quadrature; - Ordinary differential equations: - Euler, modified Euler and Runge-Kutta methods; - The finite difference method for partial differential equations: - Equations of Laplace and Poisson, - The transient heat equation. Textbooks - Zill D.G. and Cullen M.R., Advanced Engineering Mathematics, Jones and Bartlett, 3rd Edition, 2006. - 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. To be offered in and after 2009-2010: (to 2nd years of 3-year course) |
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| ADDITIONAL NOTES | Follows from: MAT1801, MAT1802 | ||||||
| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||
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| LECTURER/S | Anton Buhagiar Joseph Sultana |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
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 2025/6. It may be subject to change in subsequent years. |
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