MU10230 Mathematical Analysis II

Mathematical Institute in Opava
Summer 2014
Extent and Intensity
0/0. 7 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Marta Štefánková, Ph.D.
Mathematical Institute in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
V návaznosti na první část předmětu, pokračujeme ve studiu matematické analýzy dokončením kapitoly o nekonečných řadách. Dále následují dvě stěžejní kapitoly totiž diferenciální a integrální počet funkcí reálných funkcí jedné proměnné.
Syllabus
  • 1. Infinte series of functions. Product of series (ordinary, Cauchy). Series of functions, their pointwise and uniform convergence, continuity of the sum. Power series. Elementary functions.
    2. Differential calculus. Derivative of a function at a point, tangent to the graph, properties of derivative, chain rule, derivative of inverse function. Total differential. Derivatives of higher order. Extrema of real functions. Lagrange's and Cauchy's theorems on the increment of a function, L'Hospital rule. Taylor polynomial; Taylor series.
    3. Integral calculus. Riemann integral of a bounded function, area of the subgraph. Integrability of bounded functions. Basic properties of the integral. Integral as a function of the upper bound (primitive), integration by parts, change of variable in definite and indefinite integrals. Newton-Leibniz formula. Improper integrals. Integration of rational functions.
Literature
    recommended literature
  • M. Krupka, M. Málek. Matematická analýza I, II. MÚ SU, Opava, 2007. URL info
  • J. Holenda. Řady. SNTL-Nakladatelství technické literatury, Praha, 1990. ISBN 80-03-00505-1. info
  • D. Krupka, O. Krupková. Topologie a geometrie, 1. Obecná topologie. SPN, Praha, 1989. info
  • V. Jarník. Diferenciální počet I. ČSAV, Praha, 1963. info
  • V. Jarník. Diferenciální počet II. ČSAV, Praha, 1963. info
  • V. Jarník. Integrální počet I. ČSAV, Praha, 1963. info
  • V. Jarník. Integrální počet II. ČSAV, Praha, 1963. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
The examination consists of a written and an oral part.
The course is also listed under the following terms Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020.
  • Enrolment Statistics (Summer 2014, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2014/MU10230