Mathematical Analysis II

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Course Unit Code470-8723/01
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *First Year
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
BOU10prof. RNDr. Jiří Bouchala, Ph.D.
VOD03Mgr. Petr Vodstrčil, Ph.D.
This subject contains 2 basic themes:
differential and integral calculus of multivariable real functions.
Learning Outcomes of the Course Unit
Students will get basic practical skills for work with fundamental concepts, methods and applications of differential and integral calculus of multivariable functions.
Course Contents
1. Differential calculus of multivariable functions

Real functions of several variables.
Limits and continuity.
Partial derivative, gradient and directional derivative, total differential.
Differentials of higher orders, Taylor polynomials, Taylor's theorem.
Implicit function theorem.
Local, constrained and global extrema. Lagrange multipliers method.

2. Integration of multivariable functions

Riemann double and triple integrals.
Fubini theorem.
Substitution theorem for double and triple integrals.
Applications of double and triple integrals.
Recommended or Required Reading
Required Reading:
J. Stewart: Calculus, 2008 Thomson

J. Kuben, Š. Mayerová, P. Račková, P. Šarmanová: Diferenciální počet funkcí více proměnných,

P. Vodstrčil, J. Bouchala: Integrální počet funkcí více proměnných,
Recommended Reading:
W. Rudin: Principles of Mathematical Analysis. McGraw-Hill Book Company, New York 1964
B. Budinský, J. Charvát: Matematika II. SNTL, Praha 1990
J. Charvát, M. Hála, V. Kelar, Z. Šibrava: Příklady k Matematice II, ČVUT, Praha 1999
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 10
        ExaminationExamination70 21