MU:MU03030 Real Analysis II - Course Information

MU03030 Real Analysis II

Extent and Intensity

2/0/0. 6 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)

MU03021 Real Analysis I || MU03028 Real Analysis I || MU18023 Real Analysis I

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

• Mathematical Analysis (programme MU, M1101)
• Mathematical Analysis (programme MU, N1101)
• Mathematics (programme MU, B1101)

Course objectives (in Czech)

Náplní přednášky jsou pokročilejší partie z teorie integrálu, diferencovatelnost funkcí a vztah derivací a integrálu.

Syllabus

• Relationship between Lebesgue and Riemann integrals
  Measurability, integrability and continuity
  Generalizations, Henstock-Kurzweil integral
  Continuity and differentiability
  Differentiability of monotonous functions
  Points of discontinuity of a function
  Banach-Mazurkiewicz theorem
  Derivative of a function discontinuous on a dense set
  Functions of bounded variation
  Absolutely continuous functions
  Differentiability in normed spaces
  Approximation of real functions
  Stone-Weierstrass theorem

Literature

recommended literature
• A. M. Bruckner, J. B. Bruckner, B. S. Thomson. Real Analysis. Upper Saddle River, New Jersey, 1997. ISBN 0-13-458886-X. info
• M. Švec, T. Šalát, T. Neubrunn. Matematická analýza funkcií reálnej premennej. Bratislava, 1987. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.

• Enrolment Statistics (Summer 2014, recent)
  
• Permalink: https://is.slu.cz/course/sumu/summer2014/MU03030