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ECTS Course Overview



Mathematical Analysis 2

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code470-2111/06
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Optional
Level of Course Unit *First Cycle
Year of Study *
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech, English
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
S1A64RNDr. Petra Vondráková, Ph.D.
Summary
This subject contains following topics:
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differential calculus of two and more-variable real functions,
integral calculus of more-variable real functions or differential equations (according to the version)
Learning Outcomes of the Course Unit
Students will learn about differential calculus of more-variable real functions.
In the second part students will get the basic practical skills for working with fundamental concepts, methods and applications of integral calculus of more-variable real functions.
Course Contents
Lectures:

More-variable real functions
Partial and directional derivatives
Differential and gradient, tangent plane and linear approximations
Taylor's theorem
Extremes of more-variable real functions
Differential equations
Separable equations
Linear equations
Second order linear equations
Applications of first-order and second-order differentials equations

Exercises:

More-variable real functions - domain, level curves, graphs
Partial and directional derivatives
Differential and gradient, tangent plane and linear approximations
Taylor's theorem
Extremes of more-variable real functions
Differential equations. Separable equations
Linear equations
Second order linear equations
Applications of first-order and second-order differentials equations
Recommended or Required Reading
Required Reading:
L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973.
J. Bouchala: Matematika III, www.am.vsb.cz/bouchala, 2000.
J. Kuben, Š. Mayerová, P. Račková, P. Šarmanová: Diferenciální počet funkcí více proměnných (http://mi21.vsb.cz/modul/diferencialni-pocet-funkci-vice-promennych), 2012.
P. Vodstrčil, J. Bouchala: Integrální počet funkcí více proměnných
(http://mi21.vsb.cz/modul/integralni-pocet-funkci-vice-promennych), 2012.
B. Krajc, P. Beremlijski: Obyčejné diferenciální rovnice (http://mi21.vsb.cz/modul/obycejne-diferencialni-rovnice), 2012.
L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973.
Recommended Reading:
J. Bouchala, M. Sadowská: Mathematical Analysis I, VŠB-TUO.
J. Bouchala: Sbírka příkladů z matematické analýzy 1, 2 a 3, www.am.vsb.cz/bouchala.
J. Brabec, B. Hrůza: Matematická analýza II, SNTL, Praha, 1986.
B. Budinský, J. Charvát: Matematika II, SNTL, Praha, 1990.
L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973.
J. Bouchala, M. Sadowská: Mathematical Analysis I, VŠB-TUO.
Planned learning activities and teaching methods
Lectures, Tutorials
Assesment methods and criteria
Tasks are not Defined