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.
- recommended prerequisite
Recommended optional programme components
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
Assesment methods and criteria linked to learning outcomes
Home assignments during the semester.
The condition for receiving the credit is obtaining at least a given minimum of points from the activities during the semester.
Language of instruction
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.
Type of course unit
26 hours, optionally
Teacher / Lecturer
- The concept of a function of a real variable, properties of functions and basic operations with functions.
- Elementary functions of a real variable.
- Limit and continuity of a function. Limit of a sequence.
- Derivative and a differential of a function.
- Higher-order derivatives. Taylor polynomial. Extrema of a function.
- Graph properties.
- Interpolation and approximation.
- Numerical solutions of equations.
- Indefinite integral, basic methods of integration.
- Definite Riemann integral, its applications. Numerical integration.
- Improper integral.
26 hours, compulsory
Teacher / Lecturer
Problems discussed at numerical classes are chosen so as to complement suitably the lectures.
- Ima [.pdf] 5.29 MB
- Inm [.pdf] 2.79 MB
- Matematika_1_sbirka [.pdf] 462.58 kB
- Ism [.pdf] 1.92 MB
- Matematika_3_num [.pdf] 287.65 kB