Математический анализ. Конспек

Crib, lecture notes on the course Mathematical analysis. Theory, properties

Mathematical analysis (classical mathematical analysis) - a set of sections of mathematics corresponding to the historical section under the name "analysis of infinitesimal", combines the differential. and integral. calculus. Classical mathematical analysis is based on modern analysis, which is considered as one of the three main areas of mathematics (along with algebra and geometry).

Lecture notes on mathematical analysis:

- Basic concepts

- Faces of numerical plural

- Numeric sequences

- Converging and diverging posts

- Properties of converging posts

- Exhibitor or number e

- The principle of nested segments

- Function of one variable

- The limit of f-tion at a point. Properties of the limit of f-tion at a point

- Unilateral limits of the function in t-ke. A sign of the existence of a limit. The limit of f-tion in t-ke

- Properties of limits. Continuity of function. Limit and continuity of function

- The limit. One way limit

- The limits of the function at infinity

- Two wonderful limits

- BM functions and their comparisons

- Continuous functions. Continuity.

- Classification t-ki break

- Nepr. f-tion on the ave

- Differentiation of functions

- Pr-nye and differentials high. Of orders

- Convex and concave functions

- T-ki inflection. Bulge and concavity

- BB half. Smooth function

- Elasticity of functions

- Application of the 1st pr-in research. f-tions

- Intervals of monotonicity of the function

- Rule of Lital

- Derivative of inverse function

- Bolzano-Weierstrass Theorem

- Bolzano-Cauchy Theorem

- Weierstrass theorem