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
Written tests during the semester (maximum 30 points).
The condition for receiving the credit is active work during the semestr and obtaining at least 10 points from the tests 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 compulsory (presence at lectures, however, will not be controlled), absence at numerical classes has to be excused.
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.
- Complex numbers. Functions of a complex variable.
- Limit of a sequence. Limit and continuity of a function.
- Differential calculus of functions of one variable. Derivative at a point, derivative in an interval, a differential of a function. Numerical differentiation.
- Second derivative. Extrema of a function.
- Graph properties.
- Taylor theorem. Approximation of functions.
- Newton and Lagrange interpolation.
- Numerical solutions of nonlinear equations.
- Integral calculus of functions of one variable. 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