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Mathematical Analysis II - NMAF034

Title:	Matematická analýza II
Guaranteed by:	Laboratory of General Physics Education (32-KVOF)
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

Class:	Fyzika
Classification:	Physics > Mathematics for Physicists
Interchangeability :	NMAF052
Is incompatible with:	NMAI047, NMAI009, NMAA008, NMAA007
Is pre-requisite for:	NMAF003
Is interchangeable with:	NMAI009, NMAA002, NMAI047

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Annotation -

Last update: G_M (03.06.2004)

Second part of hte basic course of mathematics for the students of physics (bachelor study). Follows the course MAF033, a simultaneously running course MAF041 is recommended.

Aim of the course -

Last update: T_KVOF (28.03.2008)

Second part of hte basic course of mathematics for the students of physics (bachelor study). Follows the course MAF033, a simultaneously running course MAF041 is recommended.

Literature - Czech

Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

Kopáček J.: Matematika pro fyziky I.,II.,III. Skripta MFF UK

Kopáček J. a kol. : Příklady z matematiky pro fyziky I., II. Skripta MFF UK

Jarník J.: Diferenciální počet I.,II

Jarník J.: Integrální počet I

Děmidovič V.: Sbírka úloh a cvičení z matematické analýzy (rusky)

Teaching methods - Czech

Last update: T_KVOF (28.03.2008)

přednáška + cvičení

Syllabus -

Last update: G_M (03.06.2004)

1. Ordinary differential equations:

Solution of an ODE; Cauchy problem for the ODE's; basic existence and uniqueness theorems; scalar equations of the first order - basic methods of finding solutions; linear equations of the nth order - fundamental system, variation of the constant, special right-hand side.

2. Number series:

Convergent/oscilatory/divergent number series; convergence criteria for series with non-negative terms and general terms; absolute and relative convergence; product of series.

3. Sequences and series of functions:

Pointwise and uniform convergence; criteria for uniform convergence of sequences and series of functions; interchanging of limits, derivative and integral of sequences and series of functions; power series; real analytic functions.

4. Lebesgue integral:

Sigma-algebras, measures; construction of the Lebesgue measure; measurable functions; approximation of measurable fuunctions by simple functions; integral of simple non-negative functions; integral of general functions and its properties; limite passage through the integral; relations among Riemann, Newton and Lebesgue integral; integral dependent on parameters; Fubini's theorem, change of variables.