Skip to main content
Skip header

Mathematical Analysis 2

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

Course Unit Code470-2111/05
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *Second Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
KRA04Mgr. Bohumil Krajc, Ph.D.
S1A64RNDr. Petra Vondráková, Ph.D.
KRA0220Ing. Jan Kracík, Ph.D.
Summary
This subject contains following topics:
-----------------------------------
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
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit30 (30)10
                1. písemkaWritten test15 0
                2. písemkaWritten test15 0
        ExaminationExamination70 21