Czech

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 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.

he 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.

Students must first obtain the credit from seminars. Compulsory attendance at seminars. In the exercises are included 2 tests (each at most 12 points).. In total the exercises can receive a maximum of 24 points. A student has to obtain at least 6 points from each test. (Students are allowed to undergo corrective control work. Evaluation of corrective labor inspection is final.)

The exam is written. Students do not use any electronic devies during the exam, however they can use written preparation in the range of two A4 sheets.

1. Number sets, vectors, matrices. Matrix operations.
Sem. The recapitulation of selected themes of secondary schools. Introduction to matrices.
2. Linear independence, rank of matrices, determinants.
Sem. Matrix operations. Elementary row operations, rank.
3. Systems of linear equations. Frobenius theorem, Gaussian elimination, Cramer's rule.
Sem. Determinants to order 3. Systems of linear equations.
4. Geometry in E2 and E3: inner, outer and vector products. Lines and planes.
Sem. Systems of linear equations. Application of the products.
5. Geometry in E2 and E3: the role of angles and distances. Conics.
Sem. Parametric and general equations of lines and planes. Classification of conic sections and quadrics without mixed member (filling into a square).
6. Functions of one real variable. Basic features, graph. Inverse function.
Sem. TEST 1: 1) Matrix multiplication 2) Determinant 3) The system of linear equations 4) The geometry of lines and planes 5) Classification of conic sections and quadrics
7. Elementary functions: polynomials, rational functions, power functions, exponential and logarithmic functions, trigonometric functions.
Sem. Domains of elementary functions.
8. Derivative, geometric and physical meaning, calculation, chemical applications.
Sem.. Calculations of derivatives.
9. Calculations limits using of derivative (L'Hospital's rule). Taylor polynomial.
Sem. Taylor polynomial (briefly). Calculations of limits.
10. The determination of functions properties (with emphasis on the extremes).
Sem. Functions properties.
11. The method of least squares.
Cv. The method of least squares.
12. Interpolation polynomials and splines.
Cv. TEST 2: 1) Domain of functions 2) Derivative 3) [six-point example] Graphing functions
13. Summarizing lecture, discussion.
Cv. Interpolation polynomials and splines. Evaluation of seminars, granting credits.

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 compulsory attendance at seminars. In the exercises are included 2 tests (each at most 12 points). In total the exercises can receive a maximum of 24 points. A student has to obtain at least 6 points from each test.

Not applicable.

Not applicable.

Matematika online, http://mathonline.fme.vutbr.cz/ (CS)
Thomas G. B.: Calculus, Addison Wesley (EN)
Thomas G.B., Finney R.L.: Calculus and Analytic Geometry, Addison Wesley (EN)

Děmidovič B. P.: Sbírka úloh a cvičení z matematické analýzy (CS)
Rektorys K. a spol.: Přehled užité matematiky I,II ,SNTL (CS)