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Calculus IIb - NMAA074

Title:	Kalkulus IIb
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2022
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:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Classification:	Mathematics > Real and Complex Analysis
Pre-requisite :	{Math. Analysis 1a, 1b, Calculus Ia, Ib}
Incompatibility :	NMAA004
Interchangeability :	NMMA212
Is incompatible with:	NMMA212, NMMA341
Is interchangeable with:	NMMA212, NMMA341

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: prof. RNDr. Miroslav Hušek, DrSc. (30.03.2005)

Calculus for the second year of Bc. study (3. semester). Topics : complex functions, calculus of variation. Laplace and Fourier transforms

Literature - Czech

Last update: T_KMA (23.05.2008)

J. Kopáček: Matematika pro fyziky IV, V

S. Fučík, J. Milota: Matematická analýza II

B. Novák: Funkce komplexní proměnné

Syllabus -

Last update: prof. RNDr. Miroslav Hušek, DrSc. (30.03.2005)

complex functions, holomorphic functions, Taylor polynom, elementary complex functions.

Complex functions

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

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

Calculus of variations.

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

Laplace and Forier transforms

basic properties and relations, transorms of elementary functions. Inverse Laplace and Fourier transforms. Application to solution of differential equation.