Czech

7

Not applicable.

Comprehension of basic aspects of computing methods and differentiation of their various types. Realization of potentialities of computing methods, particularly from the viewpoint of their convergence and stability. The knowledge of algorithms of approximate methods including theoretical conditions for the correct application. Effective employing of mathematical software including the ability to assess the results obtained by computations. The development of the ability to apply approximate methods to solve problems from applications.

Differential calculus of functions of one and more variables, integral calculus of functions of one variable, linear algebra.

Not applied.

Instructing is divided into lectures and exercises. Lectures are focused on the theory referring to applications, exercises on practical calculations and solving of application tasks.

Requirements to obtain a closure :
" to attend exercise sessions according to the given conditions of controlled classes
" to write up a term homework assignment with a grading "E" at least
" to pass two midterm written control tests with a grading "E" at least
" to accomplish given tasks showing study activity over the course of the term with an overall grading "E" at least

The exam is composed of two parts- written and oral, whereby a written part makes the main proportion.
The length of a written part is 2 hours. There are 2 problems stated on the exam, each with a rating 50 points. Written part is evaluated as the sum of ratings of both tasks. If a student does not obtain at least 51 points out of 100, the written part and the whole exam is graded "F" and a student does not proceed to oral part. Otherwisse, written part is graded as follows : "A" - 95 up to 100 points, "B"- 85 up to 94 points, "C"-75 up to 84 points, "D"- 65 up to 74 points, "E"-51 up to 64 points.
The oral part follows the written one, its length usually does not exceed 10 minutes. Its main purpose is to precise the grading. Over the course of oral part a student has the opportunity to go through concrete evaluation of problems on written part and to comment or present complaints or explain possible confusions. If there are reasons either from teacherś side or the studentś side, the teacher may put additional questions. The student has a right to claim the time for preparation

Topics and the contents of lectures :
" General aspects of computing methods
" Errors, sources of errors and their classification
" Convergence and stability, computational complexity
" Approximate solution of algebraic and transcendental equations-bisection method, iteration methods, Laguerre method
" Approximate solution of systems of linear equations-iteration methods
" Approximate solution of systems of nonlinear equations- Gauss method
" Approximation of functions- least square method, spline method
" Monte Carlo method-application to numerical integration and solution of systems of linear equations

The contents of exercises :
" Solving of problems concerning the topics of lectures
" Writing up individual tasks using mathematical software

Not applicable.

To understand general principles and types of computing methods together with the problems of convergence and stability. To know the sources of errors, their classification and to perform the estimations of errors. To master effective approximate methods to solve algebraic and transcendental equations, systems of linear and nonlinear equations, basic methods of functions approximation, approximate methods for definite integrals and Monte Carlo methods for selected problems. To have a good command to employ mathematical software.

Attendance at lectures is not controlled. Attendance at exercises(problem sessions) is compulsory and is regularly checked. A student is obliged to give reasons for his absence. The teacher has a full competency to judge the reasons. In the affirmative, the teacher states the form of the compensation for the missed classes

Not applicable.

Not applicable.

1) Maroš, B.-Marošová, M.: Základy numerické matematiky. 1.vydání. FSI v PC-DIR Real, s.r.o., Brno 1999, 144s. ISBN 80-214-1494-4 (CS)
2) Děmidovič, B.P., Maron I.A. : Základy numerické matematiky . 1.vydání. SNTL, Praha 1966. 452s. (CS)

1) Ralston, A.: Základy numerické matematiky. 2.vydání. SNTL, Praha 1978. 455s. ISBN 80- 105- 1256-4 (CS)

20 hours, compulsory