Summary

1. Real numbers. Number sequences, limits of sequences. Upper bound and lower bound of a number set. The number e.2. Functions of a single variable. Limits of functions. Properties of continuous functions.3. Derivatives and differentials of functions. Properties of differentiable functions (Theorems of Roll, Lagrange, Cauchy) l'Hopital rules, Taylor's formula. Expansions of the functions ex, sinx, cosx, ln(1 + x), (1 + x)p Extremum of functions. Investigation of functions and a construction of graphs.4. Primitive functions and indefinite integral. Integration methods.5. Definite integral as a limit of Riemann sums. Polar coordinates. Applications of the definite integral (area of a planar figure, volume of a rotation body, length of a curve).6. Improper integral (on an unbounded interval and of unbounded functions).