| CODE | MAT2814 | |||||||||
| TITLE | Numerical Analysis with MATLAB | |||||||||
| UM LEVEL | 02 - Years 2, 3 in Modular Undergraduate Course | |||||||||
| MQF LEVEL | Not Applicable | |||||||||
| ECTS CREDITS | 4 | |||||||||
| DEPARTMENT | Mathematics | |||||||||
| DESCRIPTION | Study-unit Aims: This study-unit introduces the Matlab language to engineering students and illustrates how to use this powerful tool to solve problems in numerical analysis. A number of numerical methods are discussed, and these are then implemented to solve a variety of problems in engineering. - The Matlab language: • Description of the main commands; • Introduction to programming in Matlab; • Implementation in Matlab of simple numerical methods. - 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. - 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 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. - Implementation of most of the above numerical methods in Matlab. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Recognise the advantages and disadvantages associated with the use of numerical methods to solve problems; - Compare different methods that can be used in a given situation; - Apply relevant numerical methods to address a variety of problems; - Utilise Matlab commands to solve numerical problems; - Prepare a project using the Matlab programming language. 2. Skills: By the end of the study-unit the student will be able to: - Formulate solutions to problems by using appropriate mathematical techniques; - Evaluate the applicability of different theorems and results to engineering problems; - Address engineering problems by applying appropriate mathematical tools. Main Text/s and any supplementary readings: Textbooks: - Hahn B.D. and Valentine D.T., Essential Matlab for Engineers and Scientists, 3rd Edition, Elsevier, 2007. - Sauer T.D., Numerical Analysis, Pearson, 2006. - Fausett L.V., Applied Numerical Analysis using Matlab, 2nd Edition, Pearson, 2008. Supplementary Readings - Grasselli M. and Pelinovsky D., Numerical Mathematics, Jones and Bartlett Publishers, 2008. - Press W.H., Flannery B.P., et al., Numerical Recipes in Fortran, Cambridge University Press, 1989. - 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. - Gerald C.F. and Wheatley P.O., Applied Numerical Analysis, 6th Edition, Addison-Wesley, 1997. |
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| ADDITIONAL NOTES | Follows from: MAT1801, MAT1802 Leads to: MAT3815 |
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| STUDY-UNIT TYPE | Project | |||||||||
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| LECTURER/S | Anton Buhagiar |
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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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