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Mathematical Analysis (121011-1160):
  • Lecture - Wednesdays 13:30-15:10 in room A-8,
  • Classes - Wednesdays 15:20-17:00 in room A-8.

Books:

  • Davidson, Kenneth R., Donsig, Allan P. - Real Analysis and Applications. Theory in Practice, Springer, 2010
  • Dean Corbae Maxwell B. Stinchcombe, Juraj Zeman - An Introduction to Mathematical Analysis for Economic Theory and Econometrics, Priceton University Press, 2009
  • M. Krych - Analiza matematyczna dla ekonomistów, Wydawnictwa Uniwersytetu Warszawskiego, 2010
  • A. Birkholc - Analiza matematyczna, Funkcje wielu zmiennych, PWN, 2001
  • S. Dorosiewicz, J. Kłopotowski, D. Kołatkowski, H. Sosnowska - Matematyka, Oficyna Wydawnicza SGH, 2004
  • W. Dubnicki, J. Kłopotowski, T. Szapiro - Analiza matematyczna, podręcznik dla ekonomistów, PWN, 1999
  • M. Ekes, J. Kłopotowski - Analiza matematyczna I, teoria i zadania, Oficyna Wydawnicza SGH, 2008
  • W. Krysicki, L. Włodarski - Analiza matematyczna w zadaniach, część I i II, Państwowe Wydawnictwo Naukowe, Warszawa 2007
  • A. Ostoja-Owsiany - Matematyka w ekonomii, cześć druga, Elementarny rachunek różniczkowy, PWN, 2006
  • E. Panek - Ekonomia matematyczna, Wydawnictwo Akademii Ekonomicznej w Poznaniu, Poznań 2003
  • J. Banaś, S. Wędrychowicz - Zbiór zadań z analizy matematycznej, Wydawnictwo Naukowo-Techniczne, Warszawa 2001

Links:

Ważniak - mathematical analysis
Ważniak - linear algebra
Octave and its extension Octave-Forge with the exemplary manual

Grading Regulations:

  • One test for 50 points.
  • One exam for 50 points.
  • The grade on the basis of the sum of the test and the exam by the conversion table:
    POINTSGRADE
    < 502
    from 503
    from 603.5
    from 704
    from 804.5
    from 905
  • Cheating on tests and exams will not be tolerated. If a student get caught cheating, the test/exam will be confiscated and rated to zero points.

Course overview:

  1. Limits of infinite sequences. Infinite series - definition and convergence criteria.
  2. Applications of differential calculus of functions of one variable. L'Hospital's Rule, Taylor's formula.
  3. Integral - methods of integration. Riemann integral, improper integrals.
  4. Relations, equivalence relations, mappings.
  5. Metric spaces.
  6. Limits and continuity of mappings. The properties of continuous mappings.
  7. The convergence and the limit of sequences of mapping.
  8. Power series, Taylor series.
  9. Multivariable functions: the domain, level curves, continuity, differentiablity.
  10. Applications of the derivative of multivariable function, gradient. The second derivative and its applications: the local extrema, the constrained local extrema, the global extrema.
  11. Applications of derivatives: invertible mapping, implicit mapping.
  12. Elements of measure theory: algebra and sigma-algebra, premeasure and measure, Lebesgue measure.
  13. Measurable functions, Lebesgue integral of measurable functions.
  14. Lebesgue integral and its properties.
  15. Multiple integrals, change of variables theorem.
Contact: [email protected]