## MA018 Numerical Methods

Fakulta informatiky
podzim 2022
Rozsah
2/2/0. 3 kr. (plus ukončení). Ukončení: zk.
Vyučováno prezenčně.
Vyučující
RNDr. Veronika Eclerová, Ph.D. (cvičící)
RNDr. Lenka Přibylová, Ph.D. (cvičící)
Garance
Katedra teorie programování - Fakulta informatiky
Dodavatelské pracoviště: Ústav matematiky a statistiky - Ústavy - Přírodovědecká fakulta
Differential and integral calculus of functions of one and more variables. Basic knowledge of linear algebra, theory of matrices and solving systems of linear equations. Basics of programing.
Omezení zápisu do předmětu
Předmět je nabízen i studentům mimo mateřské obory.
Mateřské obory/plány
předmět má 18 mateřských oborů, zobrazit
Cíle předmětu
This course provides explanation of numerical mathematics as the separate scientific discipline. The emphasis is given to the algorithmization and computer implementation. Examples with graphical outputs help to explain even some difficult parts.
Výstupy z učení
At the end of course students should be able to apply numerical methods for solving practical problems and use these methods in other disciplines.
Osnova
• 1. Error analysis: absolute and relative error, representation of numbers, error propagation
• 2. Iterative methods for solving of nonlinear equations: general iterative method, order of the convergence, Newton method and its modifications
• 3. Direct methods for solving systems of linear equations: methods based on Gaussian elimination, methods for special matrices
• 4. Iterative methods for solving of systems of linear equations: general construction of iterative methods, Jacobi method, Gauss-Seidel method
• 5. Solving of systems of nonlinear equations: Newton method
• 6. Interpolation and approximation: polynomial and piece-wise polynomial interpolation, curve approximations, subdivision schemes, least squares method
• 7. Numerical differentiation: differentiation schemes
• 8. Numerical integration: methods based on interpolation, Monte Carlo integration
Literatura
doporučená literatura
• NOCEDAL, Jorge. Numerical optimization. Edited by Stephen J. Wright. 2nd ed. New York: Springer, 2006. xxii, 664. ISBN 0387303030. info
• MATHEWS, John H. a Kurtis D. FINK. Numerical methods using MATLAB. 4th ed. Upper Saddle River, N.J.: Pearson, 2004. ix, 680. ISBN 0130652482. info
• BURDEN, Richard L. a J. Douglas FAIRES. Numerical analysis. 6th ed. Pacific Grove, Calif.: Brooks/Cole, 1997. xiii, 811. ISBN 0534955320. info
• STOER, J. a R. BULIRSCH. Introduction to numerical analysis. 1. vyd. New York - Heidelberg - Berlin: Springer-Verlag, 1980. 609 s. IX. ISBN 0-387-90420-4. info
Výukové metody
Lectures: 2 hours weeky - theoretical preparation, 2 hours weekly - class excercise.
Practical exercise (2 hours) in a computer room is focused on solving of problems by methods presented in the lecture and algoritmization and programming of theese numerical methods.
Metody hodnocení
Written exam and work during the semester - 30 points together (10 points - work during the semester, 20 points - exam).
Assessment of the course:
27 points and more - A
24 points and more - B
21 points and more - C
18 points and more - D
15 points and more - E
less then 15 points - F
During the exam students are allowed to use computers and any study materials. There is no required minimum for either part (exam, work during the semester). The only requirement is to get at least 15 points in total.
Vyučovací jazyk
Angličtina
Další komentáře
Předmět je vyučován každoročně.
Výuka probíhá každý týden.
Předmět je zařazen také v obdobích podzim 2017, podzim 2018, podzim 2019, podzim 2020, podzim 2021.
• Statistika zápisu (nejnovější)