Mathematical Analysis
Course description:
This course addresses the basic notions of modern Mathematical Analysis such as set theory, real
numbers, limits, continuity, differentiability and integration. The main focus is on the theory of
functions of one and several real variables. Among other things, students will be able to
efficiently determine limits of sequences and functions, construct graphs of functions on the
plane, determine and study local and global extrema of differentiable functions.
Instructor: Chistyakov, Vyacheslav V.
Credit points: 4
Faculty: Faculty of Business Informatics and Applied Mathematics
Language: Russian
Level: Bachelor/Master
Academic hours: 112
Syllabus
1. Introduction to Analysis
2. Real Numbers
3. Limits of Sequences
4. Limits of Functions
5. Continuous Functions
6. Differential Calculus
7. Integral Calculus
8. Functions of Several Variables: Continuity
9. Functions of Several Variables: Differentiability
10. Function Series
11. Functional Spaces
12. Implicit Functions
Readings
1. Lang S. Undergraduate Analysis. Springer-Verlag, New York, 1983.
2. Zorich V.A. Mathematical Analysis, vol. 1, 2. FIZMATLIT, Moscow, 2004.