Number sets, statements, transform, functions

Natural, full, rational and real numbers and their properties, sets and essential set operations, logic conjunctives, quantifiers, negation, transform and its properties, functions.

Elementary functions

Linear, polynomial, rational, exponential, logarithmic and goniometric functions, their graphs and properties, monotony and function limitation.

Limit of a function and progression

The term limit and its definition, the limit of a function and progression and the relation between them, Heine’s theorem, limit arithmetic, limit calculation.

Derivative of a function

Derivative as a change (speed) and directive (tangent), mathematical definition of a derivative, rules for derivative calculations, the derivative of a compound function, derivative of elementary functions, L’Hosital’s rule.

Properties of continuous functions

Continuity of a function, the existence theorem of zero points, the mean value theorem, local and global extremes, exact and numeric methods for finding roots and radicals, applications.

The shape of a function

Increasing and falling functions, convex and concave functions, inflection points, asymptotes, inversion functions, cyclometric functions.

Multiple variable functions

Establishing a real function of two real variables, continuity, partial derivative, total differential, gradient, extremes.

Primitive functions

Finding a primitive function as the opposite of derivatives, properties of primitive functions, basic formulas for primitive function calculations (an integral chart), methods of integration.

Definite integrals

Definition of Newton’s definite integral, definite integral as the plane under a curve, calculating a definite integral, application to calculating volumes and superficies, numeric integration.

Progression and series

Arithmetic and geometric progression, their sum, recurrent progressions, convergent and divergent progressions, selected progressions.

Complex numbers

The algebraic form of a complex number, geometrical representation, the goniometric form, quadratic and binomial equation, the main theorem of algebra.

Polynomials and their application

Polynomial roots, methods of their exact and approximate determination, Taylor’s polynomial, Lagrange’s polynomials.