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Course, academic year 2019/2020
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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. Mgr. Robert Šámal, Ph.D.
RNDr. Dušan Pokorný, Ph.D.
doc. RNDr. Martin Klazar, Dr.
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. (18.02.2019)

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

To obtain credit from the tutorial, a student needs to satisfy both of the following conditions:

  • score at least 50% in the test at the end of the term,
  • score average 60% of credit from homework, three lowest marks/undelivered homework will not be considered into this average.

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 -
Last update: Mgr. Tereza Klimošová, Ph.D. (18.02.2019)

Exam will be written. A student must obtain credit from the tutorial to take the exam. The material for the exam corresponds to the syllabus to the extent to which topics were covered during lectures and tutorials and in reading assignments. Ability to generalize and apply theoretical knowledge to solving problems will be required.

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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