Lecturer(s)


Machalová Jitka, RNDr. Ph.D.

Kobza Jiří, doc. RNDr. CSc.

Ženčák Pavel, RNDr. Ph.D.

Burkotová Jana, Mgr. Ph.D.

Course content

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: NewtonCotes formulas, Gausstype formulas, compound formulas. Error estimates. 5. Solving systems of linear equations  direct methods (GaussJordan, matrix decompositions). 6. Iterative methods (Jacobi, GaussSeidel, 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.

Learning activities and teaching methods

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

Learning outcomes

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 Maple is also included.
Comprehension Understand the numerical methods of mathematical analysis and linear algebra.

Prerequisites

Basic knowledge of mathematical analysis and linear algebra.

Assessment methods and criteria

Oral exam, Seminar Work
Credit: 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

Recommended literature


Eldén L. (2004). Introduction to Numerical Computation. Studentliteratur.

Horová I., Zelinka J. (2004). Numerické metody. MU Brno.

Kobza J. (1993). Numerické metody. PřF UP Olomouc.

Linfield G., Penny J. (1995). Numerical Methods Using Matlab. Horwod.

Segethová J. (1998). Základy numerické matematiky. Karolinum Praha.

Vitásek E. (1982). Numerické metody. SNTL Praha.
