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Lecturer(s)
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Fajkus Martin, RNDr. Ph.D.
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Sedláček Lubomír, Mgr. Ph.D.
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Martinek Pavel, Ing. Ph.D.
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Včelař František, RNDr. CSc.
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Ulrich Adam, Ing.
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Course content
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- Primitive function and indefinite integral. Straight forward integration. Modification of integrand. - Basic methods of integration - substitution and per partes - Integration of rational functions. - Definite integral. Calculation of definite integral. - Use of definite integral. - Improper integral. - Real function of <I>n</I> real variables. Domain of definition of a function of two variables. - Partial derivatives. Differential. - Local extrema. - Constrained and global extrema. - Infinite numerical series and its sum. Geometrical series. General properties of numerical series. - Criteria of convergence of numerical series. - Alternating series. Leibnitz's criterion. - Economical applications. Using of the Maple system in solving of the problems.
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Learning activities and teaching methods
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Lecturing, Methods for working with texts (Textbook, book), Demonstration, Projection (static, dynamic), Practice exercises
- Preparation for course credit
- 20 hours per semester
- Preparation for examination
- 54 hours per semester
- Participation in classes
- 56 hours per semester
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| prerequisite |
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| Knowledge |
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| Knowlegde of the course Mathematics I. |
| Knowlegde of the course Mathematics I. |
| learning outcomes |
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| After completion of the course student: |
| After completion of the course student: |
| - defines the basic concepts of integral calculus |
| - defines the basic concepts of integral calculus |
| - clarifies basic integration methods: adjustment of integrand, substitution, per partes |
| - clarifies basic integration methods: adjustment of integrand, substitution, per partes |
| - defines a definite integral |
| - defines a definite integral |
| - clarifies the geometric meaning of a definite integral |
| - clarifies the geometric meaning of a definite integral |
| - explains the use of a definite integral in economics |
| - explains the use of a definite integral in economics |
| - defines a real function of n real variables |
| - defines a real function of n real variables |
| - clarifies the concept of the domain of a function of two variables |
| - clarifies the concept of the domain of a function of two variables |
| - defines the terms partial derivative (even higher order) and differential of a function |
| - defines the terms partial derivative (even higher order) and differential of a function |
| - recognizes local extrema and saddle points of a function |
| - recognizes local extrema and saddle points of a function |
| - applies bound and global extrema in economics |
| - applies bound and global extrema in economics |
| - defines an infinite sequence and an infinite series |
| - defines an infinite sequence and an infinite series |
| - explains the concept of convergence of an infinite series |
| - explains the concept of convergence of an infinite series |
| - defines the sum of an infinite series |
| - defines the sum of an infinite series |
| Skills |
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| After completion of the course, student is able to: |
| After completion of the course, student is able to: |
| - compute simple integrals by adjusting the integrand |
| - compute simple integrals by adjusting the integrand |
| - calculate integrals by substitution method and per partes |
| - calculate integrals by substitution method and per partes |
| - calculate definite and improper integral |
| - calculate definite and improper integral |
| - determine the area and volume of a rotating body using a definite integral |
| - determine the area and volume of a rotating body using a definite integral |
| - use the definite integral in economics |
| - use the definite integral in economics |
| - determine and draw the domain of the function of two variables |
| - determine and draw the domain of the function of two variables |
| - calculate partial derivatives (even of higher order) and differential of a function |
| - calculate partial derivatives (even of higher order) and differential of a function |
| - determine local extrema and saddle points of a function |
| - determine local extrema and saddle points of a function |
| - decide about the convergence of an infinite series |
| - decide about the convergence of an infinite series |
| - calculate the sum of an infinite series |
| - calculate the sum of an infinite series |
| teaching methods |
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| Knowledge |
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| Lecturing |
| Lecturing |
| Methods for working with texts (Textbook, book) |
| Practice exercises |
| Practice exercises |
| Projection (static, dynamic) |
| Demonstration |
| Demonstration |
| Methods for working with texts (Textbook, book) |
| Projection (static, dynamic) |
| assessment methods |
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| Grade (Using a grade system) |
| Grade (Using a grade system) |
| Written examination |
| Written examination |
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Recommended literature
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FINNEY, R., L.; THOMAS, G., B. Jr. Calculus. New York: Addison-Wesley Publishing Company, 1994.
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JANOUŠKOVÁ, L. Nekonečné řady - sbírka řešených a neřešených příkladů. Zlín, 2009.
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Kaňka, M. Henzler, J. Matematika 2. Ekopress Praha, 2003. ISBN 80-86119-77-7.
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Křenek, J., Ostravský, J. Diferenciální a integrální počet funkce jedné proměnné s aplikacemi v ekonomii. FT UTB, 2005.
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Ostravský, J. Diferenciální počet funkce více proměnných. Nekonečné číselné řady. Zlín : UTB, 2007. ISBN 978-80-7318-567-1.
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