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Lecturer(s)
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Machalová Jitka, doc. RNDr. Ph.D., MBA
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Burkotová Jana, Mgr. Ph.D.
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Radová Jana, Mgr.
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Course content
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1. Computer modelling, algorithms, errors and stability of numerical computations. 2. Approximation of functions - interpolation, least squares approximation using polynomials, splines, systems of orthogonal functions. 3. Numerical differentiation - basic formulas for numerical computing derivatives of functions of one and two variables. 4. Numerical integration: Newton-Cotes formulas, Gauss-type formulas, compound formulas. Error estimates. 5. Solving systems of linear equations - direct methods (Gauss-Jordan, matrix decompositions). 6. Iterative methods (Jacobi, Gauss-Seidel, relaxation and gradient methods) - algorithms, convergence and error estimation problems. 7. Solving nonlinear equations (bisection, regula falsi, fixed point, Newton's methods). 8. Solving systems of nonlinear equations (iterative methods, Newton's method). 9. Roots of polynomials (Horner?s scheme, root estimation and computing). 10. Computing matrix eigenvalues and eigenvectors (position estimates, decomposition and transformations of matrices, applications to difference and differential equations). 11. Methods of approximate and numerical solutions of ordinary differential equations.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
- Attendace
- 52 hours per semester
- Homework for Teaching
- 30 hours per semester
- Preparation for the Course Credit
- 15 hours per semester
- Preparation for the Exam
- 55 hours per semester
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Learning outcomes
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The course introduces basic methods of function approximation, numerical solution of linear and nonlinear equations and systems of equations, numerical differentiation and integration, and numerical solution of ordinary differential equations. Implementation of the basic methods in MatLab or Python is also included.
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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Segethová J. (1998). Základy numerické matematiky. Karolinum Praha.
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