MA018 Numerical Methods

Fakulta informatiky
podzim 2025
Rozsah
2/2/0. 3 kr. (plus ukončení). Ukončení: zk.
Vyučováno kontaktně
Vyučující
RNDr. Veronika Eclerová, Ph.D. (přednášející)
Mgr. Jakub Záthurecký, Ph.D. (cvičící)
Mgr. Jiří Zelinka, Dr. (cvičící)
Garance
Mgr. Jiří Zelinka, Dr.
Katedra teorie programování – Fakulta informatiky
Dodavatelské pracoviště: Ústav matematiky a statistiky – Ústavy – Přírodovědecká fakulta
Rozvrh
Čt 18. 9. až Čt 18. 12. Čt 18:00–19:50 A318
  • Rozvrh seminárních/paralelních skupin:
MA018/01: Út 16. 9. až Út 16. 12. Út 16:00–17:50 A320, V. Eclerová
MA018/02: Po 15. 9. až Po 15. 12. Po 16:00–17:50 A215, J. Záthurecký
MA018/03: St 17. 9. až St 17. 12. St 8:00–9:50 B204, J. Zelinka
MA018/04: St 17. 9. až St 17. 12. St 10:00–11:50 B204, J. Zelinka
Předpoklady
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 23 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. Linear algebra recapitulation, Error analysis, Matrix decomposition
  • 2. Least Square method, Interpolation (polynomial, linear and multilinear, spline)
  • 3. Systems of nonlinear equations (Newton method and its generalizations, convergence analysis)
  • 4. Iterative methods for solving of systems of linear equations (Jacobi method, Gauss-Seidel method, relaxation methods)
  • 5. Optimization in R (bisection, golden ratio, quadratic interpolation, and Newton methods)
  • 6. Optimization in R^n (Nelder–Mead, gradient descend, Newton, quasi-Newton, and conjugate gradient methods)
  • 7. Numerical integration (Newton-Cotes formulae, Gaussian quadrature formulae, Monte-Carlo integration)
  • 8. Numerical differentiation and solving ODEs (numerical estimation of derivative, solving intial value problems for ODEs and boundary value problems ODEs and PDEs)
Literatura
    doporučená literatura
  • BURDEN, Richard L.; J. Douglas FAIRES a Annette M. BURDEN. Numerical Analysis. Cengage Learning, 2015, 896 s. 10th Edition. ISBN 978-1-305-25366-7. info
  • NOCEDAL, Jorge a Stephen J. WRIGHT. Numerical optimization. 2nd ed. New York: Springer, 2006, xxii, 664. ISBN 1493937111. info
  • MATHEWS, John H. a Kurtis D. FINK. Numerical methods using MATLAB. 4th ed. Upper Saddle River: Pearson, 2004, ix, 680. ISBN 0130652482. info
  • STOER, J. a R. BULIRSCH. Introduction to numerical analysis. 3. vyd. New York: Springer, 2002, 746 s. IX. ISBN 978-0-387-95452-3. 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.
Additional information about software: The course uses GNU Octave, which is freely available and has very similar syntax to MATLAB. Some recommended materials are in MATLAB, which is why this compatibility is important. For presentation purposes, additional materials will be provided in Jupyter notebooks. Using Jupyter is optional (recommended, but not required).
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 (without internet) and any study materials (including lecture notes, books in written form or on computer, prepared codes including codes provided by teachers during semester). 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
Studijní materiály
Předmět je vyučován každoročně.
Předmět je zařazen také v obdobích podzim 2017, podzim 2018, podzim 2019, podzim 2020, podzim 2021, podzim 2022, podzim 2023, podzim 2024.
  • Statistika zápisu (nejnovější)
  • Permalink: https://is.muni.cz/predmet/fi/podzim2025/MA018