Czech

Not applicable.

After completing the course, the student should be able to:

- decide whether vectors are linearly independent and whether they form a basis of a vector space;
- add and multiply matrices, compute the determinant of a square matrix to the 4x4 type, compute the rank and the inverse of a matrix;
- solve a system of linear equations;
- estimate the domains and sketch the grafs of elementary functions;
- compute limits and asymptots for the functions of one variable, use the L’Hospital rule to evaluate limits;
- differentiate and find the tangent to the graph of a function, find the Taylor ploynomial of a function near a given point;
- sketch the graph of a function including extrema, points of inflection and asymptotes;
- integrate using technics of integration, such as substitution, partial fractions and integration by parts;
- evaluate a definite integral including integration by parts and by a substitution for the definite integral;
- compute the area of a region using the definite integral, evaluate the inmproper integral;
- discuss the convergence of the number series, find the set of the convergence for the power series.

Knowledge at secondary school level and of completed subjects in the study area

Not applicable.

Teaching methods include lectures, computer exercise and computing exercises with computer support.

The semester examination is rated at a maximum of 70 points.  It is possible to get a maximum of 30 points in practices, 10 of which are for written tests and 20 points for 2 project solutions.

1. Basic mathematical notions. Sets, operations with sets, concept of a function, inverse function, sequences.
2. Vector spaces, basic notions, linear combination of vectors, linear dependence, independence vectors, base, dimension of a vector space.
3. Matrices and determinants.
4. Systems of linear equations and their solution.
5. Differential calculus of one variable, limit, continuity, derivative of a function.
6. Derivatives of higher orders, Taylor's theorem.
7. L´Hospital's rule, behavior of a function.
8. Integral calculus of fuctions of one variable, antiderivatives, indefinite integral. Methods of a direct integration.
9. Integration by parts, substitution methods, integration of some elementary functions.
10. Definite integral and its applications.
11. Improper integral.
12. Infinite number series, convergence criteria.
13. Power series, Taylor series.

Not applicable.

The main goal of the calculus course is to explain the basic principles and methods of higher mathematics that are necessary for the study of electrical engineering. The practical aspects of application of these methods and their use in solving concrete problems (including the application of contemporary mathematical software) are emphasized.

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Not applicable.

Not applicable.

Brabec, B., Hrůza, B., Matematická analýza II, SNTL, Praha, 1986. (CS)
Kolářová, E: Matematika 1 - Sbírka úloh. (CS)
Krupková, V., Fuchs, P., Matematika 1. (CS)

Edwards, C.H., Penney, D.E., Calculus with Analytic Geometry, Prentice Hall, 1993. (EN)
Fong, Y., Wang, Y., Calculus, Springer, 2000. (EN)
Goldstein, L.J., Lay, D.C., Schneider, D.I., Asmar, N.H., Calculus & Its Applications, Pearson, 2017. (EN)
Hoffmann, L., Bradley, G., Sobecki, D., Price, M., Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition, McGraw-Hill Education, 2012. (EN)
Kolářová, E: Maple. (CS)
Lial, M.L., Greenwell, R.N., Ritchey, N.P., Calculus with Applications, Pearson, 2015. (EN)
Ross, K.A., Elementary analysis: The Theory of Calculus, Springer, 2000. (EN)
Švarc, S. a kol., Matematická analýza I, PC DIR, Brno, 1997. (CS)
Thomas, G.B., Finney, R.L., Calculus and Analytic Geometry, Addison-Wesley Publ. Comp., 1994. (EN)