Course: Numerical Methods 1

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Course title Numerical Methods 1
Course code KMA/NM1
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Machalová Jitka, RNDr. Ph.D.
  • Machů Hana, Mgr.
  • Burkotová Jana, Mgr. Ph.D.
Course content
1. Introduction to numerice methods, error analysis, condition numbers. 2. Forward, backward and dividend differences - their properties and computing. 3. Difference equations and their solution. 4. Introduction to interpolation - statement of the problem, existence and uniqueness of solution. 5. Lagrange interpolation, Newton interpolation and interpolation using function values only. 6. Error in polynomial interpolation. Chebyschev orthogonal polynomials and thein using in interpolation. 7. Iterative linear interpolation. Hermite interpolation. 8. Least squares approximation of functions and least squares approximation over discrete sets of points. 9. Numerical differentiation - formulas and error estimation. 10. Numerical integration - basic rules and notions. 11. Gaussian quadrature formulae. 12. Newton-Cotes quadrature formulae. Composite quadrature formulae.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 52 hours per semester
  • Homework for Teaching - 30 hours per semester
  • Preparation for the Course Credit - 40 hours per semester
Learning outcomes
Understand basic numerical methods of mathematical analysis.
Comprehension Understand the numerical methods of mathematical analysis.
Prerequisites
Basic knowledge of mathematical analysis and linear algebra.

Assessment methods and criteria
Written exam, Seminar Work

written test
Recommended literature
  • F. B. Hildebrand. (1987). Introduction to numerical analysis. Dover Publications.
  • I. Horová. (1999). Numerické metody. skripta MU Brno.
  • J. Kobza. (1993). Numerické metody. Skripta UP Olomouc.
  • J. Segethová. (1998). Základy numerické matematiky. Skriptum UK Praha.
  • P. Přikryl. (1995). Numerické metody. Skripta ZČU Plzeň.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science General Physics and Mathematical Physics (2014) Physics courses 1 Winter