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Course, academic year 2023/2024
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Mathematical Analysis III - NUMP012
Title: Matematická analýza III
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2011
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Class: Učitelství matematiky
Classification: Mathematics > Real and Complex Analysis
Teaching > Mathematics
Interchangeability : NUMP021
Is incompatible with: NMAA004, NMAA003
Annotation -
Last update: T_KMA (15.05.2001)
The lecture is devoted to the introduction to complex analysis.
Literature - Czech
Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

J. Veselý: Komplexní analýza pro učitele. Karolinum, Praha 2000

B. Novák: Funkce komplexní proměnné (pro učitelské studium MFF), SPN, Praha

I. Černý: Základy analysy v komplexním oboru, Academia, Praha

W. Rudin: Reálná a komplexní analýza, Academia, Praha

Syllabus -
Last update: T_KMA (22.05.2003)

1. Complex field C, complex functions of real variable. Complex functions of complex variable, derivative, Cauchy-Riemann equations. Riemann sphere.

2. Holomorphic functions. Elementary functions (linear fractional transformations, exp, sin, cos, tg, cotg, sinh, cosh, tgh, cotgh). Argument and logarithm of complex numbers. Paths in C, integral over paths in C and its (in)dependence on a path. Cauchy's theorem.

3. Cauchy's formula and its corollaries (Liouville's theorem, fundamental theorem of algebra, existence and uniqueness of power series representation of holomorphic functions).

4. Laurent series, Cauchy's formula in an annulus, existence and uniqueness Laurent series representation. Isolated singularities of holomorphic functions. Residue theorem, computation of integrals using residue theorem.

5. Meromorphic functions.

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