|
Lecturer(s)
|
-
Fajkus Martin, RNDr. Ph.D.
|
|
Course content
|
- Primitive function and indefinite integral. Straight forward integration. Modification of integrand. - Integration of rational functions. Basic methods of integration. - Definite integral. Calculation of definite integral. - Use of definite integral. Improper integral. - Real function of <I>n</I> real variables. Domain of a function of two variables. - Partial derivatives. Differential. - Local extrema. - Constrained and global extrema. - Infinite numerical series and its sum. Geometric series. General properties of numerical series. - Criteria of convergence of numerical series. - Alternating series. Leibnitz's criterion. - Economical applications.
|
|
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 completing the course, the student in particular: - defines the basic terms of integral calculus - clarifies basic integration methods: simplification of integrand, substitution, per partes - defines a definite integral - clarifies the geometric meaning of a definite integral - explains the use of a definite integral in economics - defines a real function of n real variables - clarifies the term domain of a function of two variables - defines the terms of partial derivative (even of higher order) and differential of a function - recognizes local extrema and saddle points - applies bound and global extremes in economics - defines an infinite sequence and an infinite series - explains the concept of convergence of an infinite series - defines the sum of an infinite series |
| After completing the course, the student in particular: - defines the basic terms of integral calculus - clarifies basic integration methods: simplification of integrand, substitution, per partes - defines a definite integral - clarifies the geometric meaning of a definite integral - explains the use of a definite integral in economics - defines a real function of n real variables - clarifies the term domain of a function of two variables - defines the terms of partial derivative (even of higher order) and differential of a function - recognizes local extrema and saddle points - applies bound and global extremes in economics - defines an infinite sequence and an infinite series - explains the concept of convergence of an infinite series - defines the sum of an infinite series |
| define basic terms of integral calculus |
| define basic terms of integral calculus |
| use the method by parts, method of substitution and partial fraction decomposition |
| use the method by parts, method of substitution and partial fraction decomposition |
| define and calculate the definite integral |
| define and calculate the definite integral |
| apply the definite integral in geometry and economics |
| apply the definite integral in geometry and economics |
| define a real function of n real variables and find the domain of definition of functions of two variables |
| define a real function of n real variables and find the domain of definition of functions of two variables |
| define and calculate partial derivatives and differentials, higher orders including |
| define and calculate partial derivatives and differentials, higher orders including |
| find local, constrained and global extrema of functions of two variables and apply them in economics |
| find local, constrained and global extrema of functions of two variables and apply them in economics |
| decide about a convergence of infinite numerical series |
| decide about a convergence of infinite numerical series |
| find the sum of geometrical series |
| find the sum of geometrical series |
| use the Leibnitz's criterion for alternating series |
| use the Leibnitz's criterion for alternating series |
| find the radius and the domain of convergence of a power series |
| find the radius and the domain of convergence of a power series |
| apply the term of infinite numerical series in financial mathematics |
| apply the term of infinite numerical series in financial mathematics |
| Skills |
|---|
| After completing the course, the student in particular: - computes simple integrals by simplifying the integrand - calculates integrals by substitution methods and per partes - calculates definite and improper integral - determines the area and volume of a rotational body using a definite integral - uses a definite integral in economics - determines and draws the domain of a function of two variables - calculates partial derivatives (even of higher order) and differential of a function - determines local extrema and saddle points of a function of two variables - decides the convergence of an infinite series - calculates the sum of an infinite series |
| After completing the course, the student in particular: - computes simple integrals by simplifying the integrand - calculates integrals by substitution methods and per partes - calculates definite and improper integral - determines the area and volume of a rotational body using a definite integral - uses a definite integral in economics - determines and draws the domain of a function of two variables - calculates partial derivatives (even of higher order) and differential of a function - determines local extrema and saddle points of a function of two variables - decides the convergence of an infinite series - calculates the sum of an infinite series |
| compute simple integrals by simplifying the integrand |
| compute simple integrals by simplifying 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 rotational body using a definite integral |
| determine the area and volume of a rotational body using a definite integral |
| determine and draw the domain of a function of two variables |
| determine and draw the domain of a 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 of two variables |
| determine local extrema and saddle points of a function of two variables |
| 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 |
|---|
| Demonstration |
| Lecturing |
| Lecturing |
| Practice exercises |
| Demonstration |
| Methods for working with texts (Textbook, book) |
| Methods for working with texts (Textbook, book) |
| Projection (static, dynamic) |
| Projection (static, dynamic) |
| Practice exercises |
| 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 Lucie. Nekonečné řady sbírka řešených a neřešených příkladů. Zlín, 2009.
-
Kaňka, M. Henzler, J. Matematika 2. Ekopress Praha, 2003. ISBN 80-86119-77-7.
-
Křenek, Josef. Diferenciální a integrální počet funkce jedné proměnné s aplikacemi v ekonomii. Vyd. 4. Zlín : Univerzita Tomáše Bati, Fakulta technologická, 2004. ISBN 8073181630.
-
Matejdes, Milan. Aplikovaná matematika. Zvolen, 2005. ISBN 80-89077-01-3.
-
Ostravský, J. Diferenciální počet funkce více proměnných. Nekonečné číselné řady. Zlín : UTB, 2007. ISBN 978-80-7318-567-1.
|