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.
Supervisor
Department
Learning outcomes of the course unit
The ability to understand the basic problems of calculus and use derivatives and integrals for solving specific problems.
Prerequisites
Secondary school mathematics.
- recommended prerequisite
Co-requisites
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.
Aims
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
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
- 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.
- Improper integral.
- Numerical integration.
Computer-assisted exercise
26 hours, compulsory
Teacher / Lecturer
Syllabus
Problems discussed at numerical classes are chosen so as to complement suitably the lectures.
E-learning texts
- 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