Czech

4

Not applicable.

The knowledge and skills will appear on the following fields
1. Students will manage successfully a work with matrices and solving systems of linear equations.
2. Students will be endowed with the knowledge of elementary functions and their properties. Students are expected to manage the concept of a limit and derivative and comprehend their meaning.They master their computation applying basic rules including the L´Hospital rule. Students will also be able to investgate the course of a function of one variable.
3. Students will be endowed with the knowledge of the indefinite and definite integral including the improper integral. They learn the basic methods of integral computations and be aquaitanced with the basic applications.
4. Students will be acquainted with the simpliest kinds of differential equations and the methods of their solution and also with the applications.
5. Students obtain the ability of solving simple tasks of the physical character and tasks occuring in the advanced courses.

Elementary knowledge of mathematics on the level of the secondary school. Linear and quadratic equations, inequalities, elements of
the geometry of lines and planes.

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

A course-credit unit is obtained on the base of a regular an active participation on practices and obtaining the required number of marks from three tests written during the semester. Obtaining a credit is a necessary condition for siting for the examination, which consists of the test ond an oral part. Results from practices are included to the total rating of the subject.

1. The concept of a vector space with the linear independency and the basis. Elementary ways of giving planes and a lines in the space.
2. Polynomials and other elementary functions with their basic properties.
3. Matrices and elementary operations on matrices, the concept of the rank and determinant.
4. Elementary concepts of the calculus of functions of one variable - the limit, derivative and a continous function. A geometrical, physical and chemical meaning of the derivative, L'Hospital rule, a computation of a derivative of elementary functions by means of formulas and rules.
5. Inverse matrices, systems of linear equations, the Gauss elimination method.
6. The concept of a differential and its applications, Taylor polynomial and its applications.
7. The complete investigation of a function.
8. The indefinite integral and the elementary methods of its computation - the per partes and the substitution method.
9. The integration of a rational function and some irational functions, the universal trigonometric substitution.. The definite integral.
10. The improper integrals, geometrical and physical applications of a definite integral.
11. Elementary concepts of the theory of ordinary differential equations (ODE's) and the computation of the simpliest kinds of first-order ODE's, i.e. separable and linear equations.
12. Higher-order linear differential equations with constant coefficients. The method of indefinite coefficients for the special right side.
13. Foundations of the analytical geometry of planary and spatial quadratic objects, the least square method.

Not applicable.

The aim of the course is making acquitance with the basic concepts of mathematics necessary for managing the following courses of physics, chemistry and engineering disciplines. Another claim is obtaining the basic principles of mathematical thinking and skills and applying them in the above mentioned courses.

The regular participation on practices and obtaining at least 50% of marks from each of three control tests form the necessary conditions for obtaining the credit. In control works, not only computation skills are checked but also the ability of their application to simple practical problems. Besides the claim of a succesfull passing the tesst for a credit, a student is motivated for obtaining the maximum of marks since the marks from the practices are included to the complex rating of the subject. If a student fails at a control test, he has a possibility of its correction.

Not applicable.

Not applicable.

Škrášek J., Tichý Z.: Základy aplikované matematiky 1 SNTL Praha 1989, ISBN 80-03-00150-1 (CS)
Karásek J., Mezník I.: Matematika pro strojní fakulty. SNTL Praha (CS)
Švarc S., Krupková V., Studená V.: Matematická analýza I. Skriptum VUT Brno (CS)
Bayer J., Polcerová M.: Analytická geometrie v příkladech. Skriptum FCH VUT v Brně (CS)
Veselý P., Matematika pro bakaláře. VŠCHT Praha (CS)

Bican L.: Lineární algebra. Academia Praha (CS)
Karásek J.: Matematika II. Skriptum FSI VUT v Brně (CS)
Eliáš J., Horváth J., Kajan J., Šulka R.: Zbierka úloh z vyššej matematiky. ALFA Bratislava (CS)
Rektorys K.: Přehled užité matematiky, díl I, II. Prometheus Praha. (CS)
Bubeník, F.: Mathematics for Engineers. ČVUT Praha (CS)
Howard A., Irl B., Stephen D.: Calculus. John Wiley and Sons (CS)
Jordan, D.W., Smith, P.,: Mathematical Techniques. Oxford (CS)

26 hours, compulsory