Course detail

Mathematics 1

FEKT-BPA-MA1Acad. year: 2026/2027

Basic mathematical notions. Function, inverse function, polynomials. 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

English

Number of ECTS credits

7

Mode of study

Not applicable.

Guarantor

doc. RNDr. Michal Novák, Ph.D.

Department

Department of Mathematics (UMAT)

Offered to foreign students

Of all faculties

Entry knowledge

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.

Rules for evaluation and completion of the course

Maximum 20 points per semester for two written tests. In order to get the credit, at least 8 points out of 20 must be obtained.

The condition for passing the exam is to obtain at least 50 points out of a total of 100 possible (20 can be obtained for work in the semester, 80 can be obtained at the final written exam).

Absence in practical classes must be apologized.

 

Aims

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.
After completing the course, students should be able to:

- 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.

Study aids

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)

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme BPA-ELE Bachelor's

    specialization BPA-ECT , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization BPA-PSA , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core

Type of course unit

 

Lecture

52 hours, optionally

Teacher / Lecturer

doc. RNDr. Michal Novák, Ph.D.

Syllabus

1. Basic mathematical concepts, functions, inverse functions, polynomials.
2. Limits and continuity of functions, asymptotes.
3. Derivatives of functions of one variable.
4. L'Hôpital's rule.
5. Higher-order derivatives, Taylor polynomials.
6. Local extrema of functions of one variable, convexity and concavity.
7. Curve sketching.
8. Integration of functions of one variable, antiderivatives, indefinite integrals, direct integration.
9. Integration by parts, substitution method, integration of selected elementary functions.
10. Definite integrals and their applications.
11. Improper integrals.
12. Infinite series, convergence tests.
13. Power series, Taylor series.

Exercise in computer lab

22 hours, compulsory

Teacher / Lecturer

Mgr. Jiří Vítovec, Ph.D.

Syllabus

1. Basic mathematical concepts, functions, inverse functions, polynomials.
2. Limits and continuity of functions, asymptotes.
3. Derivatives of functions of one variable, L'Hôpital's rule.
4. Higher-order derivatives, Taylor polynomials.
5. Local extrema of functions, convexity and concavity, curve sketching.
6. Integration of functions of one variable, antiderivatives, indefinite integrals, direct integration.
7. Integration by parts, substitution method, integration of selected elementary functions.
8. Definite integrals and their applications.
9. Improper integrals.
10. Infinite series, convergence tests.
11. Power series, Taylor series.

Project

4 hours, compulsory

Teacher / Lecturer

Mgr. Jiří Vítovec, Ph.D.

Syllabus

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

Elearning

eLearning: currently opened course