Course detail

Calculus 1

FIT-IMA1Acad. year: 2020/2021

Limit, continuity and derivative of a function. Extrema and graph properties. Approximation and interpolation. Indefinite and definite integrals.

Learning outcomes of the course unit

The ability to understand the basic problems of calculus and use derivatives and integrals for solving specific problems.


Secondary school mathematics.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Krupková, V., Fuchs, P., Matematická analýza pro FIT, elektronický učební text, 2019.
Knichal, V., Bašta, A., Pišl, M., Rektorys, K., Matematika I, II, SNTL Praha, 1966. (in Czech).
Fong, Y., Wang, Y., Calculus, Springer, 2000.
Ross, K. A., Elementary analysis: The Theory of Calculus, Springer, 2000.
Small, D. B., Hosack, J. M., Calculus (An Integrated Approach), McGraw-Hill Publ. Comp., 1990.
Thomas, G. B., Finney, R. L., Calculus and Analytic Geometry, Addison-Wesley Publ. Comp., 1994.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Home assignments during the semester.
Exam prerequisites:
The condition for receiving the credit is obtaining at least a given minimum of points from the activities during the semester.

Language of instruction

Czech, English

Work placements

Not applicable.


The main goal of the course is to explain the basic principles and methods of calculus. The emphasis is put on handling the practical use of these methods for solving specific tasks.

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

Classes are not compulsory.

Classification of course in study plans

  • Programme BIT Bachelor's, 1. year of study, summer semester, 4 credits, compulsory

  • Programme IT-BC-3 Bachelor's

    branch BIT , 1. year of study, summer semester, 4 credits, compulsory

Type of course unit



26 hours, optionally

Teacher / Lecturer


  1. The concept of a function of a real variable, properties of functions and basic operations with functions.
  2. Elementary functions of a real variable.
  3. Limit and continuity of a function. Limit of a sequence.
  4. Derivative and a differential of a function.
  5. Higher-order derivatives. Taylor polynomial. Extrema of a function.
  6. Graph properties.
  7. Interpolation and approximation.
  8. Numerical solutions of equations.
  9. Indefinite integral, basic methods of integration.
  10. Definite Riemann integral, its applications.
  11. Improper integral.
  12. Numerical integration.

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer


Problems discussed at numerical classes are chosen so as to complement suitably the lectures.

E-learning texts

Krupková, V., Fuchs, P., Matematická analýza pro FIT (cs)
Fajmon, B., Hlavičková, I., Novák, M., Vítovec, J., Numerická matematika a pravděpodobnost (cs)
Kolářová, E., Matematika 1 - Sbírka úloh (cs)
Krupková, V., Matematický seminář pro FIT (cs)
Novák, M., Matematika 3 - Sbírka příkladů z numerických metod (cs)