Mathematical analysis (part 2) - free course from Stepik, training 18 lessons, Date: December 3, 2023.

The course is a studio video recording of the second half of the first semester and the beginning of the second semester of lectures on mathematical analysis in the form in which they are given at the Academic university. Over the course of 4 modules, students will become familiar with the basic concepts of mathematical analysis: derivatives, antiderivatives and definite integrals. We will limit ourselves only to real-valued functions of one variable. The presentation will be conducted at a fairly elementary level without possible generalizations that do not change the main ideas of the evidence, but significantly complicate perception. All statements will be strictly proven. The video recordings are accompanied by a large number of tasks for students to work independently. The course is a continuation of the course “Mathematical Analysis (Part 1)”.

Initial requirements

Students who have completed the first part of the course obviously have the necessary knowledge to complete the second part.

Further information for those who are going to start straight from the second part. It is necessary to have a good command of the school mathematics curriculum. Namely, you need to know what the graphs of basic elementary functions look like, know the basic formulas for trigonometric, exponential and logarithmic functions, for arithmetic and geometric progressions, as well as confidently be able to do algebraic transformations with equalities and with inequalities. Know the definition of the limit of a sequence and a function (including one-sided limits), their arithmetic properties, remarkable limits, sum of series, Cauchy criterion, Weierstrass and Bolzano-Cauchy equivalent theorems functions.