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Course, academic year 2018/2019
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Mathematical Analysis II - NMAI055
Title in English: Matematická analýza II
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. RNDr. Martin Klazar, Dr.
doc. Mgr. Robert Šámal, Ph.D.
RNDr. Dušan Pokorný, Ph.D.
Class: Informatika Bc.
Classification: Mathematics > Real and Complex Analysis
Annotation -
Last update: doc. RNDr. Pavel Töpfer, CSc. (26.01.2018)
Course in mathematical analysis for students of computer science (informatics) covering Riemann integral, differential calculus in several variables and elements of metric spaces.
Course completion requirements -
Last update: Mgr. Tereza Klimošová, Ph.D. (20.02.2018)

Final exam is written. To take the final exam it is necessary to obtain credit from tutorial.

During tutorial, there will be two tests for 35 points each and homework for 30 points in total. To obtain the credit from tutorial, the student must satisfy these conditions:

  • obtain at least 60 points from tests, homework and work during tutorials or obtain at least 50 points and solve proportional amount of extra assignments
  • at most three absences

Literature -
Last update: doc. RNDr. Martin Klazar, Dr. (26.11.2012)

T. M. Apostol, Mathematical Analysis, Addison-Wesley, 1974 (2nd edition).

Ch. Ch. Pugh, Real Mathematical Analysis, Undergraduate Text in Mathematics, Springer, 2002.

T. Tao, Analysis I, Hindustan Book Agency, 2006.

T. Tao, Analysis II, Hindustan Book Agency, 2006.

V. A. Zorich, Mathematical Analysis I, Universitext, Springer, 2004.

V. A. Zorich, Mathematical Analysis II, Universitext, Springer, 2004.

Requirements to the exam - Czech
Last update: Mgr. Tereza Klimošová, Ph.D. (20.02.2018)

Požadavky ke zkoušce odpovídají sylabu předmětu v rozsahu, v jakém byl pokryt na přednáškách a cvičeních. Je požadována i schopnost zobecnit a aplikovat získané znalosti.

Zápočet je nutnou podmínkou pro konání zkoušky.

Syllabus -
Last update: doc. RNDr. Pavel Töpfer, CSc. (26.01.2018)

Antiderivatives (properties, calculus).

Riemann's integral (definition, properties, the fundamental theorem of calculus).

Applications of integrals (areas and volumes, applications in physics, estimates of sums and series, integral representations of functions).

Introduction to the theory of metric spaces

(definitions, basic examples-especially euclidean spaces, open and closed sets, continuous maps,

definition of topological space).

Differential calculus in several variables (partial derivatives, differential, local extrema, the implicit function theorem, extrema with constraints).

Multiple Riemann's integral (definition, Fubini's theorem).

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