The course aims to equip students with basic knowledge of mathematical analysis. Students should acquire basic computational skills relevant to the functions of one variable. Lectures are focused on the interpretation of the concepts of the differential and integral calculus.

Knowledge: The student is able to sketch graphs of elementary functions using the differential calculus. He also knows how to find an antiderivative to a given elementary function and how to evaluate a definite integral.

Skills: Students can search for extremal values of functions of one variable and determine other specific properties related to the first or the second derivative of the given function. They know the application of the calculus in physics, geometry and signal processing.

Course contents:

• Basic facts from the propositional logic and the set theory.


• Real and complex functions of one real variable, elementary functions.


• Limit and continuity of a function.


• Derivative, geometric and physical interpretation of the first derivative, calculation of derivatives.


• Mean value theorems, 1'Hospital's rule, asymptotes of a function.


• Monotony, convexity, and concavity of a function.


• Extreme points of a function.


• Antiderivative and indefinite integral. Integration by parts, a method of substitution.


• Definite integral and its applications.


• Sequences and infinite number series, various criteria for convergence of a series.


• Sequences and series of functions, power series.


• Approximation of a function, Taylor polynomial, Taylor series.


• Fourier series


• Introduction to the theory of complex functions of one complex variable