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Course, academic year 2023/2024
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Calculus 4 - NMMA212
Title: Kalkulus 4
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: summer
E-Credits: 8
Hours per week, examination: summer s.:4/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Class: M Bc. FM
M Bc. FM > Povinné
M Bc. FM > 2. ročník
Classification: Mathematics > Real and Complex Analysis
Pre-requisite : {At least one 1st year Calculus course}
Co-requisite : NMMA211
Incompatibility : NMAA074
Interchangeability : NMAA074, NMMA341
Is incompatible with: NMMA341
Is interchangeable with: NMMA341, NMAA074
Annotation -
The fourth part of a four-semester course in calculus for bachelor's program Financial Mathematics.
Last update: G_M (16.05.2012)
Course completion requirements -


Credit will be awarded after the elaboration of tasks (see the link below).

Gaining credit is a condition for taking the exam.

The form of the exam will be full-time or distance and will always be specified in the SIS for individual dates.

The full-time form of the exam will take place as in previous semesters (see the link below).

The distance form of the exam will take place in the Zoom environment and will be a modification of the full-time form.

Everything is described in more detail on the page

Last update: Pyrih Pavel, doc. RNDr., CSc. (31.01.2021)
Literature -

J. Kopáček: Matematika pro fyziky IV, V

S. Fučík, J. Milota: Matematická analýza II

B. Novák: Funkce komplexní proměnné

Last update: Pyrih Pavel, doc. RNDr., CSc. (28.10.2019)
Teaching methods -


Last update: Pyrih Pavel, doc. RNDr., CSc. (31.01.2021)
Requirements to the exam -

see Course completion requirements

Last update: Pyrih Pavel, doc. RNDr., CSc. (31.01.2021)
Syllabus -
Complex functions

Power series and its convergence radius, derivative and integral of power series.

Holomorphic functions, Cauchy-Riemann conditions, primitive functions, curve integral, Cauchy theorem,, Cauchy formula, Liouville theorem, power expansions of holomorphic functions, uniqueness theorem. Laurent series, residues and their application to integrals of real functions. Gamma function on complex numbers.

Laplace and Fourier transforms

Basic properties and relations, transforms of elementary functions. Inverse Laplace and Fourier transforms. Application to solution of differential equations.

Calculus of variations.

Extremal values of L(y)=Integral( f(x,y(x),y'(x)) , dx) and Euler equations, isoperimetrical problems.

Last update: T_KMA (30.09.2013)
Entry requirements -

Previous knowledge of Kalkulus 1 and 2 and 3 will be useful.

Last update: Pyrih Pavel, doc. RNDr., CSc. (28.10.2019)
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