Subjects(version: 945)
Mathematical Analysis II - NMAF034
Title: Matematická analýza II Laboratory of General Physics Education (32-KVOF) Faculty of Mathematics and Physics from 2022 summer 8 summer s.:4/2, C+Ex [HT] unlimited unlimited no no cancelled Czech full-time full-time
Class: Fyzika Physics > Mathematics for Physicists NMAF052 NMAI047, NMAI009, NMAA008, NMAA007 NMAF003 NMAI009, NMAA002, NMAI047
 Annotation - ---CzechEnglish
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 - ---CzechEnglish
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 - ---CzechEnglish
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.

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