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Course, academic year 2017/2018
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Mathematical Analysis II - NMAI055
Czech title: Matematická analýza II
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
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: Mgr. Tereza Klimošová, Ph.D.
Mgr. Petr Honzík, Ph.D.
Class: Informatika Bc.
Classification: Mathematics > Real and Complex Analysis
Annotation -
Last update: T_KAM (11.05.2009)

Course in mathematical analysis for students of computer science (informatics) covering Riemann integral, differential calculus in several variables and elements of metric spaces.
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.

Syllabus -
Last update: T_KAM (11.05.2009)

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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