MA018 Numerical Methods

Faculty of Informatics
Autumn 2020
Extent and Intensity
2/2/0. 3 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)
Hana Válková (assistant)
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
Mon 12:00–13:50 A318
  • Timetable of Seminar Groups:
MA018/01: Mon 14:00–15:50 A215, J. Zelinka
MA018/02: Wed 8:00–9:50 A215, J. Zelinka
MA018/03: Wed 10:00–11:50 A215, J. Zelinka
MA018/04: Fri 10:00–11:50 A215, V. Eclerová
MA018/05: Fri 12:00–13:50 A215, V. Eclerová
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
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. 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.
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 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.
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 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2020, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2020/MA018