Czech

8

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 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 test ond an oral part. Results from practices are included to the total rating of the subject.

1. The concept of a vector space,the concepts of the linear independency and the basis, coordinates of a vector with respect to a given basis.
2. Complex numbers, their algebraic and trigonometric form, algebraic operations over them. Polynomials, their division with the remainder, fundamental theorem of algebra and its consequences for polynomial decomposition over reals and complexes.
3. Matrices and elementary operations on matrices. Elementary transformations on them, Gauss elemination alghoritm, the rank of a matrix. The correspondence of those concepts with the concepts on vector spaces. MATLAB commands for algebraic operations over matrices and searching for the upper and lower triangular matrices.
4. MATLAB commands for work with complex numbers and polynomials (convolution, deconvolution with the remainder, searching for roots). The concept of a rational function, its decomposition to the sum of a polynomial and the residual rational function including the corresponding MATLAB commands.
5. Inverse matrices and determinants and their computations including MATLAB commands. Mappings and its significant kinds, properties and the existence of the inverse map.
6. Elementary functions of one variable - graphs, cyclometrical functions. MATLAB commands for drawing graphs of elementary functions. The concepts of the limit, a continous functions, and the derivative. The geometrical meaning of the derivative, its fundamental physical meaning and some examples of applications in chemistry.
7.Computation of derivatives of elementary functions bz means of the elementary formulas and rules. The L´Hospital rule, Taylor polynomial and its applications.
5. Inverse matrices, systems of linear equations, the Gauss elimination method.
8. The concept of a differential and its applications, Taylor polynomial and its applications.
7. The complete investigation of a function.
8. Investigating the of the course of a function, applications of MATLAB commands.
9. Systems of linear equations, the matrix form of the notation, the criterion of the solvability, the structure of the space of all solutions, free unknowns and the choice of parameters, the Cramer rule. The connections with tasks from analytical geometry.
10. Dot and vector products, the applications in geometry and physics.
11. the indefinite integral and the elementary computation methods - the per partes and substitution methods. The integration of trigonometric and rational functions.
12. The integration of some irational functions, the universal trigonometric substitution.. The definite integral, its definition, computation and applications.
13. The improper integrals, both the continous and discrete least square methods.
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. Students are recommended to use MATLAB when passing the second test and the tasks in the test are suitably selected for this purpose. 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.
Students are exceptionally allowed passing a credit in the summer semester but only in case of serious healthy or family reasons .

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