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Lecturer(s)
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Radová Jana, Mgr.
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Machalová Jitka, doc. RNDr. Ph.D., MBA
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Burkotová Jana, Mgr. Ph.D.
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Course content
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1. Finite differences, their properties and computing. 2. Polynomial interpolation - statement of the problem, existence and uniqueness of a solution. Lagrange interpolation, Newton interpolation and interpolation using function values only. 3. Least squares approximation over discrete sets of points. 4. Numerical differentiation - formulae and error estimation. 5. Numerical integration - basic rules and notions, Newton Cotes quadrature formulae and their using. 6. Systems of linear equations - direct elimination methods. Triangular factorization of matrices. 7. Iterative methods for systems of linear equations. 8. Methods for solving nonlinear equations. Iterative methods for solving nonlinear equations and their convergence. 9. Iterative methods for solving systems of nonlinear equations. 10. Roots of polynomials and their computations. 11. Methods for determining eigenvalues and eigenvectors.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
- Attendace
- 52 hours per semester
- Semestral Work
- 25 hours per semester
- Preparation for the Exam
- 45 hours per semester
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Learning outcomes
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The course introduces basic numerical methods of analysis and algebra.
Comprehension Understand the numerical methods of mathematical analysis and linear algebra.
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Prerequisites
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Basic knowledge of mathematical analysis and linear algebra.
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Assessment methods and criteria
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Oral exam, Seminar Work
Credit: active participation, the student has to pass written tests, seminary work Exam: the student has to understand the subject and be able to prove the principal results
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Recommended literature
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Čermák L., Hlavička R. (2016). Numerické metody. Brno: Akademické nakladatelství CERM, s.r.o.
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Eldén L. (2004). Introduction to Numerical Computation. Studentliteratur.
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Horová I., Zelinka J. (2004). Numerické metody. MU Brno.
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Linfield G., Penny J. (1995). Numerical Methods Using Matlab. Horwod.
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S. Míka. (1995). Numerické metody. Skripta ZČU Plzeň.
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Segethová J. (1998). Základy numerické matematiky. Karolinum Praha.
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