MU01001 Mathematical Analysis I

Mathematical Institute in Opava
Winter 2012
Extent and Intensity
3/0/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Marta Štefánková, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Marta Štefánková, Ph.D.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU01901 Mathematical Analysis I - Exe || MU01911 Mathematical Analysis I - Exer
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
The course is the first part of the basic course in mathematical analysis. The subject of this course is the one dimensional real function analysis, the main topics are sequences, completeness property, series and local and global behavior of functions.
Syllabus
  • 1. Real numbers and monotone sequences (real numbers, increasing sequences, limit of an increasing sequence, decreasing sequences, completeness property)
    2. Estimations and approximations (inequalities, estimations, proving boundedness, absolute values, approximations, the terminology "for n large"
    3. The limit of a sequence (definition, uniqueness of limits, infinite limits, limit of a^n)
    4. The error term (definition, the error in geometric series)
    5. Limit theorems for sequences (limits of sums, products and quotients, comparison theorems, subsequences)
    6. The completeness property (nested intervals, cluster points of sequences, the Bolzano - Weierstrass theorem, Cauchy sequences, completeness property for sets)
    7. Infinite series (series and sequences, elementary convergence tests, the convergence of series with negative terms, ratio and n-th root tests, the integral test, series with alternating signs - Cauchy's test, rearranging the terms of a series)
    8. Power series (definition, radius of convergence, addition of power series, multiplication of power series)
    9. Functions of one variable (functions, albebraic operations on functions, some properties of functions, inverse functions, the elementary functions)
    10. Local and global behavior (intervals, local behavior, local and global properties of functions)
Literature
    required literature
  • A. P. Mattuck. Introduction to Analysis. Prentice Hall, New Jersey, 1999. info
    recommended literature
  • L. Zajíček. Vybrané úlohy z matematické analýzy. Matfyzpress, Praha, 2000. info
  • REKTORYS, K. a kol. Přehled užité matematiky I, II. Praha. SNTL, 1995. ISBN 80-85849-92-5. info
  • K. Polák. Přehled středoškolské matematiky. SPN, 1991. info
  • V. Novák. Diferenciální počet v R. MU, Brno, 1989. info
  • F. Jirásek, E. Kriegelstein, Z. Tichý. Sbírka příkladů z matematiky. SNTL, Praha, 1989. info
  • R. A. Adams. Single Variable Calculus. Addison-Weseley Publischers Limited, 1983. info
  • J. Bečvář. Seznamte se s množinami. SNTL, 1982. info
  • L. Leithold. The Calculus with Analytic Geometry. Harper & Row, 1981. info
  • S. I. Grossman. Calculus. Academic Press, 1977. info
  • V. Jarník. Diferenciální počet I. 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 of an oral part.
The course is also listed under the following terms Winter 1997, Winter 1998, Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021.
  • Enrolment Statistics (Winter 2012, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2012/MU01001