Course: Mathematics E2

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Course title Mathematics E2
Course code AUM/1MAT2
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Sousedíková Lucie, Ing.
  • Hrabec Dušan, Ing. Ph.D.
  • Hýl Pavel, Mgr.
  • Fajkus Martin, RNDr. Ph.D.
  • Sedláček Lubomír, Mgr. Ph.D.
  • Martinek Pavel, Ing. Ph.D.
  • Volaříková Jana, Mgr. Ph.D.
  • Včelař František, RNDr. CSc.
Course content
- 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.

Learning activities and teaching methods
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 - 40 hours per semester
prerequisite
Knowledge
Knowlegde of the course Mathematics I.
Knowlegde of the course Mathematics I.
learning outcomes
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
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
Knowledge
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
Grade (Using a grade system)
Grade (Using a grade system)
Written examination
Written examination
Recommended literature
  • FINNEY, R., L.; THOMAS, G., B. Jr. Calculus. New York: Addison-Wesley Publishing Company, 1994.
  • JANOUŠKOVÁ, L. Nekonečné řady - sbírka řešených a neřešených příkladů. Zlín, 2009.
  • Kaňka, M. Henzler, J. Matematika 2. Ekopress Praha, 2003. ISBN 80-86119-77-7.
  • Křenek, J., Ostravský, J. Diferenciální a integrální počet funkce jedné proměnné s aplikacemi v ekonomii. FT UTB, 2005.
  • Ostravský, J. Diferenciální počet funkce více proměnných. Nekonečné číselné řady. Zlín : UTB, 2007. ISBN 978-80-7318-567-1.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester