| CODE | MAT3805 | ||||||
| TITLE | Optimisation, Complex and Numerical Analysis 1 | ||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||
| MQF LEVEL | Not Applicable | ||||||
| ECTS CREDITS | 4 | ||||||
| DEPARTMENT | Mathematics | ||||||
| DESCRIPTION | - Optimisation: - Local and global extrema of functions of several variables, - Lagrange’s method for constrained problems, - Lagrange’s method with two constraints; - Functions of a complex variable: - Notation and definitions, - Limits, continuity and analytic functions, - The Cauchy-Riemann equations, - Exponential, trigonometric, hyperbolic, logarithmic and power functions, - Harmonic functions. - Numerical Analysis: - Locating roots of equations: - The Newton Raphson 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, - Bairstow’s method for the quadratic factors of a polynomial with real coefficients, - The quotient difference method for the roots of a polynomial; - Solution of linear equations: - Gaussian elimination, - Cholesky’s LU and LLT methods, - Iterative methods: Jacobi, Gauss-Seidel and the SOR methods; - Eigenvalues and eigenvectors: - Bounds for eigenvalues using Gershgorin’s theorem, - The power method for the largest and smallest eigenvalues, and the corresponding eigenvectors, - Rayleigh’s quotient for Hermitean matrices, - Jacobi’s method of rotations for real symmetric matrices, - Applications to quadratic forms and normal modes. 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., Teukolsky S.A. and Vetterling W.T., Numerical Recipes in Fortran, Cambridge University Press, Cambridge, 1989. - Rajasekaran S., Numerical Methods in Science and Engineering, 2nd Edition, Wheeler Publishing, 1991. - 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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| ADDITIONAL NOTES | Follows from: MAT1801, MAT1802 | ||||||
| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||
| METHOD OF ASSESSMENT |
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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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