MA018 Numerical Methods

Faculty of Informatics
Autumn 2024
Extent and Intensity
2/2/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
RNDr. Veronika Eclerová, Ph.D. (lecturer)
Mgr. Jakub Záthurecký, Ph.D. (seminar tutor)
Mgr. Jiří Zelinka, Dr. (seminar tutor)
Guaranteed by
Mgr. Jiří Zelinka, Dr.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 25. 9. to Wed 18. 12. Wed 14:00–15:50 D2
  • Timetable of Seminar Groups:
MA018/01: Tue 24. 9. to Tue 17. 12. Tue 16:00–17:50 A320, V. Eclerová
MA018/02: Wed 25. 9. to Wed 18. 12. Wed 10:00–11:50 B204, J. Záthurecký
MA018/03: Thu 26. 9. to Thu 19. 12. Thu 8:00–9:50 A215, J. Zelinka
MA018/04: Thu 26. 9. to Thu 19. 12. Thu 10:00–11:50 A215, J. Zelinka
Prerequisites
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.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
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.
Learning outcomes
At the end of course students should be able to apply numerical methods for solving practical problems and use these methods in other disciplines.
Syllabus
  • 1. Linear algebra recapitulation, Error analysis, Matrix decomposition
  • 2. Least Square method, Interpolation (polynomial, linear and multilinear, radial base, 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, two-grid method)
  • 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)
Literature
    recommended literature
  • NOCEDAL, Jorge and Stephen J. WRIGHT. Numerical optimization. 2nd ed. New York: Springer, 2006, xxii, 664. ISBN 1493937111. info
  • MATHEWS, John H. and Kurtis D. FINK. Numerical methods using MATLAB. 4th ed. Upper Saddle River, N.J.: Pearson, 2004, ix, 680. ISBN 0130652482. info
  • BURDEN, Richard L. and J. Douglas FAIRES. Numerical analysis. 6th ed. Pacific Grove, Calif.: Brooks/Cole, 1997, xiii, 811. ISBN 0534955320. info
  • STOER, J. and R. BULIRSCH. Introduction to numerical analysis. 1st ed. New York - Heidelberg - Berlin: Springer-Verlag, 1980, 609 pp. IX. ISBN 0-387-90420-4. info
Teaching methods
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.
Assessment methods
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.
Language of instruction
English
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023.
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