- explain basic concepts about mathematics.
- explain real numbers and real line, intervals, the absolute value,equations and inequalities involving absolute values,cartesian coordinates in the plane. incerements and distances.
- express straight lines, equations of lines.
- express graphs of quadratic equations.
- explain functions, the domain convention and range, graphs of functions.
- explain foundations of analyses according to limit and integration.
- describe limits of sequences.
- explain limits of functions, sequences and cauchy definitions.
- recognize infinity smools and large, operations with them.
- express features of limits of functions.
- explain basis of continuous functions.
- recognize and explain the theorems about zero, interval value and extremum value of continuous functions.
- solve some examples.
- finds the equation of the straight line tangent to a given curve at a point
- finds solutions of initial value problems
- interprets the mean value theorem geometrically.
- express basis of derivation.
- express differentations rules.
- express the mean-value theorem.
- recognize high-order derivations.
- apply the concept of derivative to related rates and extreme value problems and sketch the graph of a function.
- solves the related-rates problems
- finds extreme values of a function
- determines the intervals of concavity of a function.
- sketches the graph of a function.
- finds the linear approximation of a function at a given point.
- evaluates indeterminate forms.
- finds the Taylor polynomial of a function at a point.