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Lecturer(s)
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Sedláček Lubomír, Mgr. Ph.D.
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Řezníčková Jana, Mgr. Ph.D.
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Course content
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1. Metric spaces. 2. The concept of a function of several variables and its domain. 3. Limit and continuity of a function of several variables. 4. Partial derivatives. Derivatives in direction, gradient. 5. Derivatives of higher orders, Total differential. 6. Higher order differentials, Taylor polynomial. 7. Local extremes. 8. Bound extremes. 9. Global extremes. 10. Implicit functions. 11. Basic properties and calculation of double integral. 12. Transformations and applications of double integrals. 13. Basic properties and calculation of triple integral. 14. Transformations and applications of triple integrals.
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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, Individual work of students
- Preparation for course credit
- 20 hours per semester
- Preparation for examination
- 40 hours per semester
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| prerequisite |
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| Knowledge |
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| Knowledge of the basic mathematical apparatus of differential and integral calculus of a function of one variable is assumed. |
| Knowledge of the basic mathematical apparatus of differential and integral calculus of a function of one variable is assumed. |
| learning outcomes |
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| explain the concept of Euclidean metric |
| explain the concept of Euclidean metric |
| define the concept of a real function of two real variables, the domain of definition of a function of two real variables and the domain of values of a function of two real variables |
| define the concept of a real function of two real variables, the domain of definition of a function of two real variables and the domain of values of a function of two real variables |
| describe the geometric meaning of the partial derivatives of a function of two variables at a point |
| describe the geometric meaning of the partial derivatives of a function of two variables at a point |
| explain the meaning of the gradient at a point |
| explain the meaning of the gradient at a point |
| explain the meaning of the differential and the Taylor polynomial |
| explain the meaning of the differential and the Taylor polynomial |
| describe the process of finding local and global extrema of a function of two variables |
| describe the process of finding local and global extrema of a function of two variables |
| state the applications of the double integral |
| state the applications of the double integral |
| describe the meaning of polar coordinates |
| describe the meaning of polar coordinates |
| state the applications of the triple integral |
| state the applications of the triple integral |
| describe the meaning of cylindrical and spherical coordinates |
| describe the meaning of cylindrical and spherical coordinates |
| Skills |
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| sketch the domain of a function of two variables |
| sketch the domain of a function of two variables |
| calculate partial derivatives of functions of two variables |
| calculate partial derivatives of functions of two variables |
| construct the equation of the tangent plane to the graph of a function of two variables at a point |
| construct the equation of the tangent plane to the graph of a function of two variables at a point |
| find the stationary points of a function of two variables and use the Sylvester decision criterion to decide on the type of local extremum |
| find the stationary points of a function of two variables and use the Sylvester decision criterion to decide on the type of local extremum |
| to find global extrema on a compact set |
| to find global extrema on a compact set |
| describe simple integration areas (square, rectangle, triangle, area between graphs of elementary functions) using inequalities |
| describe simple integration areas (square, rectangle, triangle, area between graphs of elementary functions) using inequalities |
| calculate the double integral in Cartesian coordinates |
| calculate the double integral in Cartesian coordinates |
| convert the appropriate double integral to polar coordinates and integrate |
| convert the appropriate double integral to polar coordinates and integrate |
| calculate the triple integral in Cartesian coordinates |
| calculate the triple integral in Cartesian coordinates |
| convert a suitable triple integral into cylindrical or spherical coordinates and integrate |
| convert a suitable triple integral into cylindrical or spherical coordinates and integrate |
| teaching methods |
|---|
| Knowledge |
|---|
| Demonstration |
| Lecturing |
| Lecturing |
| Individual work of students |
| Demonstration |
| Methods for working with texts (Textbook, book) |
| Methods for working with texts (Textbook, book) |
| Projection (static, dynamic) |
| Projection (static, dynamic) |
| Practice exercises |
| Practice exercises |
| Individual work of students |
| 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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DEMIDOVIČ, B. P. Sbírka úloh a cvičení z matematické analýzy. Havlíčkův Brod : Fragment, 2003. ISBN 80-7200-587- 1.
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FIALKA, M. Diferenciální počet funkcí více proměnných s aplikacemi. Zlín : UTB, 2004. ISBN 80-7318-223-8.
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FIALKA, M. Integrální počet funkcí více proměnných s aplikacemi. Zlín : UTB, 2004. ISBN 80-7318-224-6.
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LIAL, M. L., T. W. HUNGERFORD a J. P. HOLCOMB. Finite mathematics with applications: in the management, natural, and social sciences. 9th ed.. Boston: Pearson/Addison Wesley, 2007. ISBN 0321386728.
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OSTRAVSKÝ, J. Diferenciální počet funkce více proměnných, nekonečné číselné řady. UTB ve Zlíně, 2007.
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RILEY, K. F., M. P. HOBSON a S. J. BENCE. Mathematical methods for physics and engineering. 3rd ed.. New York: Cambridge University Press, 2006. ISBN 9780521679718.
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WEIR, M. D., J. HASS, G. B. THOMAS a R. L. FINNEY. Thomas' calculus. 11th ed., media upgrade. Boston: Pearson/Addison-Wesley, 2008. ISBN 9780321489876.
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