Czech

6

Not applicable.

The knowledge and skills obtained during the course will appear on the following fields:
Students manage the classification and solution of the simpliest kinds of first-order differential equations and the n-th order linear differential equations with constant coefficients. They will master its solution by the method of the variation of constants and by the method of improper coefficients. Passing the course, students are able follow and apply the methods of differential calculus of n variables. In more details, they learn to find, describe and express domains, graphs, contour lines of functions. They master the concepts of a limit, partial and direction derivative and total differential with their properties.

Differential and integral calculus of functions of one variable, elements of the linear algebra and analytical geometry.

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.

First, students must have the credit from the seminar. The mandatory attendance on seminars. There are included 2 tests (each at most 10 points) and a semestral work from the computer support (5 points). In total, one can receive a maximum of 25 points. A student has to obtain at least 5 points from each test. (Students are allowed to attend correction test. The evaluation of the correction test is final.)

The exam is written.

1 Systems of linear equations. Frobenius theorem, Gauss elimination, Cramer's rule.
2 The vector space Rn (especially n = 2, n = 3). Innne, outer and cross products - features and applications. Linear and quadratic forms, classification of quadratic forms, Sylvester criterion.
3 Functions of several variables. Basic concepts, domain, graph (contour and level surfaces), limit and continuity.
4 Partial derivatives, directional derivatives, total and partial differentials, the equation of the tangent plane and normal to the graph function.
5 Partial derivatives and differentials of higher orders. Taylor polynomial.
6 Local extremes.
7 Constrained and global extremes.
8 Double and triple integrals - definition and calculation on elementary areas by Fubini's theorem.
9 Substitution theorem, polar, cylindrical and spherical coordinates.
10 Application of double and triple integrals.
11 Ordinary differential equations - basic notions (general and particular solutions, the initial problem, boundary value problem). ODE1 - Introduction (existence and uniqueness of solutions of the initial problem).
12 ODE1 - analytical solution methods (separation of variables, linear equations, variation of constants, substitution method - homogeneous functions, Bernoulli equation).
13 ODE1 - numerical methods (one-step methods, multistep methods, type predictor-corrector).

Not applicable.

The aim is to create a theoretical basis for the study of physics, especially mastering multivariate calculus and basic types of differential equations.

The mandatory attendance on seminars. There are included 2 tests (each at most 10 points) and a semestral work from the computer support (5 points). In total, one can receive a maximum of 25 points. A student has to obtain at least 5 points from each test.

Not applicable.

Not applicable.

Škrášek J., Tichý Z: Základy aplikované matematiky III. SNTL Praha. (CS)
Škrášek J., Tichý Z.: Matematika 1,2. SNTL Praha. (CS)
Polcerová, M.: Matematika II v chemii a v praxi, skripta. FCH VUT v Brně, Brno. (CS)
Veselý P.: Matematika pro bakaláře. VŠCHT Praha. (CS)
Rektorys K.: Přehled užité matematiky I, II. Prometheus Praha. (CS)
Polcerová M., Polcer J.: Sbírka příkladů z matematiky II. FCH VUT v Brně, Brno. (CS)

Eliáš J., Horváth J., Kajan J., Šulka R.: Zbierka úloh z vyššej matematiky. ALFA Bratislava. (CS)
Ivan, J.: Matematika 2. Alfa Bratislava. (CS)
Kosmák, L., Potůček, R., Metrické prostory, Academia 2004, ISBN 80-200-1202-8 (CS)
Bubeník F.: Mathematics for Engineers. ČVUT Praha. (CS)
Smith, R., Minton, R.B.: Calculus - Early Trancscendental Functions. MacGraw Hill, New York. (CS)
Mortimer, R.: Mathematics for Physical Chemistry. Academic Press, Memphis. (CS)

39 hours, compulsory