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Course, academic year 2018/2019
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Mathematical Analysis 1b - NMAA002
Title in English: Matematická analýza 1b
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2012
Semester: summer
E-Credits: 8
Hours per week, examination: summer s.:4/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech
Teaching methods: full-time
Classification: Mathematics > Real and Complex Analysis
Incompatibility : NMAA007, NMAA008
Interchangeability : NHIU076, NMAF034, NMMA102, NUMP002
Is incompatible with: NMMA102
Is interchangeable with: NMMA102
In complex pre-requisite: NMAA003, NMAA004, NMAA069, NMAA070, NMAA074
Annotation -
Last update: T_KMA (17.05.2004)
Differentiation and integration of functions of a real variable. The Newton integral and the Riemann integral. Series with complex terms. Basic facts on differentiation of functions of several variables.
Literature -
Last update: T_KMA (27.05.2008)
BASIC LITERATURE

V. Jarník: Diferenciální počet I, Academia 1984

V. Jarník: Diferenciální počet II, Academia 1984

V. Jarník: Integrální počet I, Academia 1984

B. P. Děmidovič: Sbírka úloh a cvičení z matematické analýzy, Fragment 2003

P. Holický, O. Kalenda: Metody řešení vybraných úloh z matematické analýzy pro 2.-4. semestr, Matfyzpress 2006

J. Milota: Matematická analýza I, 1. a 2. část (skriptum), MFF UK 1978

L. Zajíček: Vybrané partie z matematické analýzy pro 2. ročník, Matfyzpress 2003, 2007

L. Zajíček: Vybrané úlohy z matematické analýzy pro 1. a 2. ročník, Matfyzpress 2006

COMPLEMENTARY READING

J. Čerych a kol.: Příklady z matematické analýzy V (skriptum), MFF UK 1983

P. Holický, O. Kalenda: Metody řešení vybraných úloh z matematické analýzy pro 2.-4. semestr, Matfyzpress 2006

J. Lukeš a kol.: Problémy z matematické analýzy (skriptum), MFF UK 1982

I. Netuka, J. Veselý: Příklady z matematické analýzy III (skriptum), MFF UK 1977

W. Rudin: Principles of mathematical analysis, McGraw-Hill 1976

Syllabus -
Last update: T_KMA (22.05.2003)

1. Mean value theorems and its consequences

a) The l'Hospital rule

b) Taylor polynomials, theorems on remainders

c) Taylor series of elementary functions

2. Primitive functions (antiderivatives)

a) Integration by different methods: per-partes, substitution

b) Integration of rational functions

c) Some special substitutions

d) Application on some simple differential equations

3. The Newton and the Riemann integral

a) Definition and basic properties of the Riemann integral

b) Fundamental theorem of calculus, the existence of a primitive functions of a continuous function

c) The Newton integral and its existence/convergence. Mean value theorems

4. Series

a) Rearrangement of series. Generalized series. The Cauchy product of series

b) Convergence tests (the comparison test, Cauchy's tests, the integral test)

c) Properties of power series. The radius of convergence. Term-by-term differentiation of the series

5. Functions of several variables - basic properties

a) Continuity and limits of functions of several variables.

b) Differentiation of functions of several variables, chain rule

c) Simple implicit function theorem

 
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