|Axioms of the set of real numbers, intervals, supremum and infimum of the set.. Real functions of one variable. Basic elementary functions. The concept of a series and the limit value of a series. Monotonicity and sequence boundedness. Some important limes. Number e. Limit value (limes) of the function, definite and indefinite forms of the limes of the function. Continuity of function. The first derivative and its geometric interpretation. Differentiation rules. Differential of a function. Theorems on mean values of differential calculus. Monotonicity and extreme values of the function. Lopital's rule. Derivatives of higher order, convexity . Taylor's and MacLauren's formula. Asymptotes of functions. Graphing a function. The concept of indefinite integral, properties, direct integration. Shift method, partial entry method. Integration of rational functions, integration of some irrational functions, integration of trigonometric functions.
The concept of definite integral and properties. Newton-Leibnitz formula. Improper integral. Application of the definite integral.|