Course detail

Mathematics 1

FEKT-BPA-MA1Acad. year: 2022/2023

Basic mathematical notions. Function, inverse function, sequences. Linear algebra and geometry. Vector spaces, basic notions,linear combination of vectors, linear dependence, independence vectors, base, dimension of a vector space. Matrices and determinants. Systems of linear equations and their solution. Differential calculus of one variable, limit, continuity, derivative of a function. Derivatives of higher orders, l´Hospital rule, behavior of a function. Integral calculus of fuctions of one variable, antiderivatives, indefinite integral. Methods of a direct integration. Integration by parts, substitution methods, integration of some elementary functions. Definite integral and its applications. Improper integral. Infinite number series, convergence criteria. Power series, Taylor theorem, Taylor series.

Language of instruction


Number of ECTS credits


Mode of study

Not applicable.

Offered to foreign students

The home faculty only

Learning outcomes of the course unit

After completing the course, students 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.


Students should be able to work with expressions and elementary functions within the scope of standard secondary school requirements; in particular, they shoud be able to transform and simplify expressions, solve basic equations and inequalities, and find the domain and the range of a function.


Not applicable.

Planned learning activities and teaching methods

Teaching methods include lectures, exercises and project solving.

Assesment methods and criteria linked to learning outcomes

Maximum 20 points for completing regular assignments during the semester. The exam can be taken only if the score is 20. The exam is awarded by maximum 80 points.

Course curriculum

1. Sets, functions and the inverse function.
2. Vectors and matrices.
3. Determinants, systems of linear equations.
4. Limits and the continuity of the functions of one variable.
5. The derivative of the functions of one variable.
6. The Taylor polynom and the l'Hospitalovo rule.
7. Graphing a function.
8. Antiderivatives, the per partes method and the substitution technic.
9. Integration of the rational functions.
10. Definite integral.
11. The aplications of the definite integral and the improper integral.
12. Series.
13. Power series and Taylor series.

Work placements

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.

Specification of controlled education, way of implementation and compensation for absences

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Krupková, V., Fuchs, P., Mathematics 1, 2014, page 1-324 (EN)

Recommended reading

Edwards, C.H., Penney, D.E., Calculus with Analytic Geometry, Prentice Hall, 1993. (EN)
Fong, Y., Wang, Y., Calculus, Springer, 2000. (EN)


Classification of course in study plans

  • Programme BPA-ELE Bachelor's

    specialization BPA-ECT , 1. year of study, winter semester, compulsory
    specialization BPA-PSA , 1. year of study, winter semester, compulsory

Type of course unit



52 hours, optionally

Teacher / Lecturer


1. Basic mathematical notions, function, sequence.
2. Vector - combination, dependence and independence of vectors, base and 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 order, Taylor theorem.
7. L'Hospital rule, behaviour of a function.
8. Integral calculus of functions of one variable, primitive function, indefinite integral. Methods of direct integration.
9. Per partes method and substitution method. Integration of some elementary functions.
10. Definite integral and its applications.
11. Improper integral.
12. Infinite number series, convergence criteria.
13. Power series, Taylor theorem, Taylor series.

Exercise in computer lab

22 hours, compulsory

Teacher / Lecturer


1. Graphs of elementary functions, inverse functions, .
2. Matrices, determinants.
3. Solving a system of linear equations.
4. Derivative of a function of one variable.
5. Behaviour of a function.
6. Calculation of indefinite and definite integrals.
7. Series.


4 hours, compulsory

Teacher / Lecturer


The subject will be thought in the form of individual projects.