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13M081OPNA - Selected Topics in Numerical Analysis

Course specification
Course title Selected Topics in Numerical Analysis
Acronym 13M081OPNA
Study programme
Module
Type of study master academic studies
Lecturer (for classes)
Lecturer/Associate (for practice)
Lecturer/Associate (for OTC)
    ESPB 6.0 Status elective
    Condition Mathematics 1 (OO1MM1), Mathematics 2 (OO1MM2)
    The goal Introducing students to operator calculus and theory of approximation, ways of choosing appropriate approximations depending on nature of problem, with application in electrical engineering and computer science.
    The outcome Students are able to apply algorithms of numerical analysis in vocational subjects, to choose appropriate approximations depending on nature of problem that they are solving and to handle error.
    Contents
    Contents of lectures Operator calculus: Differential and difference operators. Generating special numbers. Three-partite recurrence Stirling numbers and generalizations. Theory of approximation: The approximation of continuous functions by polynomials. Chebyshev polynomials and minimax approximation. The Remez algorithm and implementation. The least squares approximation. Computer packages for function approximation.
    Contents of exercises Through examples, tasks and problems student learns how to apply theorems and basic concepts that are learnt through theoretical contents. Especially students are prepared how to solve problems that are occurring in vocational electrotechnical subjects.
    Literature
    1. D. Tošić: Introduction to numerical analysis, Belgrade 1997.
    2. G. Milovanović: Theory of approximation for the students of the fifth semster of the Faculty of Mathematics in Niš 2004 / G.Mastroianni, G.V.Milovanović: Interpolation Processes - Basic Theory and Applications, Springer Verlag 2004.
    3. G.E.Andrews, R.A.Askey, R.Roy: Special Functions, Cambridge University Press, Cambridge, 1999.
    4. G.-C. Rota, P. Doubilet: Finite operator calculus, Academic Press 1975.
    5. E.W.Cheney: Introduction to Approximation Theory, American Mathematical Society Bookstore 1998.
    Number of hours per week during the semester/trimester/year
    Lectures Exercises OTC Study and Research Other classes
    3 1
    Methods of teaching Combination of traditional presentation on blackboard, slides, free mathematical software (SAGE, GeoGebra,…) communication with students through internet and individual work with students while working on home work tasks, and explanation of current topics.
    Knowledge score (maximum points 100)
    Pre obligations Points Final exam Points
    Activites during lectures 0 Test paper 50
    Practical lessons 0 Oral examination 0
    Projects
    Colloquia 0
    Seminars 50