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Course, academic year 2023/2024
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Mathematical Analysis IIb - NMAI050
Title: Matematická analýza IIb
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2005
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2, C+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
Guarantor: doc. RNDr. Petr Holický, CSc.
Classification: Mathematics > Real and Complex Analysis
Interchangeability : {UMP006 and UMP012}
Co-requisite : NMAI009, NMAI049
Is incompatible with: NMAF004, NMAF003
Annotation -
Last update: T_KMA (17.05.2001)
Introductory course for students of informatics covering line and surface integrals, introduction to complex analysis and introduction to the theory of Fourier series.
Syllabus -
Last update: T_KMA (15.05.2003)

I. Path and surface integral, Stokes theorem.

II. Fundaments of the complex analysis.

Holomorphic functions, Cauchy theorem. Cauchy formula and its corollaries. Liouville theorem, fundamental theorem of algebra. Taylor series, elementary functions, Laurent series. Residua.

III. Fourier series

L2 space, Fourier series in L2, orthonormal basis, examples. Bessel inequality, Parseval equality. Pointwise convergence of trigonometric series of functions of real variable.

 
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