Czech

8

Not applicable.

The knowledge and skills will appear on the following fields
1. Students will manage successfully a work with matrices.
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 elementary commands of MATLAB and will be able to apply them for computations.
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.

The course uses teaching methods in form of Lecture - 2 teaching hours per week, seminars - 2 teaching hours per week. The e-learning system (LMS Moodle) is available to teachers and students.

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 written test. Results from practices are included to the total rating of the subject.

1. Numbers, expressions, equations. Number sets, expressing numbers, percentages.
2. Sequences. Limit of sequences.
3. The functions of one real variable. Basic properties, graphs. Inverse functions.
4. Derivative, its geometric and physical meaning, evaluations, applications.
5. Basic properties of functions - with an emphasis on the extremes.
6. Taylor polynomial. Infinite series (elementary approach, without the convergence criteria.) Taylor series.
7. Functions derived from the data (polynomial interpolations, splines, least squares method).
8. Curves given parametrically.
9. The primitive function and the indefinite integral. Basic methods of integration.
10. The definite integral, Newton and Riemann definition. Geometric and physical applications of integrals.
11. Vectors and matrices. Linear independence, rank of matrices, determinants.
12. Matrix Algebra with applications (translation, rotation). The inverse matrix.
13. Geometry of E2 and E3. Selected tasks with applications in chemistry.

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.

Attendance at seminars is obligatory, at lectures recommended.
Credit requirements: In seminars are 2 written tests (each at most 12 points) and a semestral work from the computer support (up 1 point). In total in the exercises can receive a maximum of 25 points. Students have to obtain at least 6 points from each written test.
The exam is written.

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)

39 hours, compulsory