MA018 Numerical Methods

Faculty of Informatics
Autumn 2018
Extent and Intensity
2/2/0. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
RNDr. Veronika Eclerová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 8:00–9:50 B204
  • Timetable of Seminar Groups:
MA018/01: Mon 17. 9. to Mon 10. 12. Mon 14:00–15:50 A219, J. Zelinka
Prerequisites
Differential calculus of functions of one and more variables. Basic knoledge of linear algebra-theory of matrices and solving systems of linear equations.
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
there are 16 fields of study the course is directly associated with, display
Course objectives
This course together with the course Numerical Methods II provides complete explanation of numerical mathematics as the separate scientific discipline. The emphasis is given to the algorithmization and computer implementation. Some 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 e.g. in statistical methods.
Syllabus
  • 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
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.
Theoretical exercise (1 hour) is focused on solving of problems by methods presented in the lecture, practical exercise (1 hour) in a computer room is aimed at algoritmization and programming of presented numerical methods.
Assessment methods
Written exam and work during the semester - 30 points together.
Assessment of the course:
more then 27 points - A
more then 24 points - B
more then 21 points - C
more then 18 points - D
15 points and more - E
less then 15 points - F
Language of instruction
English
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2017, Autumn 2019, Autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2018, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2018/MA018