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Terminated in academic year 2020/2021

Repetition of Mathematical Analysis

Type of study Bachelor
Language of instruction English
Code 470-2112/02
Abbreviation RMA
Course title Repetition of Mathematical Analysis
Credits 8
Coordinating department Department of Applied Mathematics
Course coordinator prof. RNDr. Jiří Bouchala, Ph.D.

Subject syllabus

Lectures:
1. Basic ideas of set theory.
2. Cardinality of sets.
3. Real numbers.
4. Sequences, limit of sequence.
5. Infinite series, criteria for convergence.
6. Exponential function, goniometric functions.
7. Sequence of functions, convergence.
8. Continuities of functions.
9. Differentiation of function . Implicit function theorem.
10. Extremes of function.
11. Weierstrass theorem .
12. Taylor´s polynomial.
13. Riemann integral.
14. Integration of functions of several real variables.

Literature

J. Bouchala, M. Sadowská: Mathematical Analysis I, http://am.vsb.cz/bouchala
W. Rudin: Principles of Mathematical Analysis, McGraw-Hill, Inc.

Advised literature

H. Anton, I. Bivens, S. Davis: Calculus, John Wiley & sons, Inc.