Scheda programma d'esame
ISTITUZIONI DI ANALISI NUMERICA
DARIO ANDREA BINI
Programma non disponibile nella lingua selezionata
KnowledgeThe student who successfully completes the course will have the ability to look at problems in approximation theory and in differential equation from the computational point of view. He/she will have the tools and the capabilities to learn more advanced and specific tools and algorithmic solutions. He/she will have the basis concepts needed for performing the design and analysis of algorithms and for approaching research topics.
Assessment criteria of knowledgeThe student will be assessed on his/her demonstrated ability - to discuss the main course contents using the appropriate terminology - to solve exercises - to relate and compare different topics and techniques encountered in the course
- Final oral exam
- Final written exam
Delivery: face to face
- attending lectures
- individual study
Syllabus1- Orthogonal polynomials: properties, interplay with tridiagonal matrices; specific polynomials: Gegenbauer, Chebyshev, Legendre, Hermite polynomials; 2- Approximation of continuous function. Best approximation in Banach and in Hilbert spaces. Computational aspects. Spline functions 3- Numerical integration 4- Numerical treatment of partial differential equations by means of finite differences methods: The Poisson problem, the heat equation, the wave equation.
BibliographyRecommended reading includes the following works R. Bevilacqua, D.A. Bini, M. Capovani, O. Menchi, Metodi Numerici, Zanichelli, 1992 D.A. Bini, M. Capovani, O. Menchi, "Metodi numerici per l'algebra lineare", Zanichelli, 1988. Eugene Isaacson and Herbert Bishop Keller, Analysis of Numerical Methods. Jhon Wiley \& Sons, Inc., New York, 1966. R.J. LeVeque. Finite Differences Methods for Ordinary and Partial Differential Equations. SIAM 2007. W. Rudin, Real and Complex Analysis, Second Edition, Tata McGraw-Hill, 1974. J. Stoer, R. Burlisch, Introduction to Numerical Analysis, Third Edition, Springer, 2002. Lectures notes supplied by the lecturer
Ultimo aggiornamento 14/11/2016 17:27