Derivative

Here you will learn what is derivative, its geometrical and physical interpretations. You will learn and practice the calculation of derivatives from definition.

Calculation of derivatives

Here you will learn the derivatives of all elementary functions. You will practice in calculation of derivatives for composite functions.

Integrals

Here you will get familiar with the concept of integral. You will learn that it has two appearances: as an area under the function and the function, whose derivative equals to the given function.

Tasks requiring derivatives

You will get familiar to two classes of tasks requiring the derivative: calculation of maximum or minimum values, and calculation of the functions that represent a derivative of the given function.

Tasks requiring integrals

Here you will get familiar with diverse types of tasks requiring integrals. In particular, you will understand this through the calculation of average value.

Preliminary test

In this test you will practice passing the final test. Most of the tasks presented here, will be offered for solution in the final test.

Sequences

In this session you will learn the concept of sequence. You will get familiar with one of the most important sequence, Taylor’s expansion.

Functions of many variables

Here you will understand that functions can be of many variables. You will get familiar with the gradient as a generalization of derivative to the multi-dimensional case.

Other types of integrals

Here you will learn other interesting types of integrals, such as integrals on the contour, or in closed three-dimensional volume.

Summarizing

This session will be devoted to the questions, and to the repeating the tasks similar to that offered in the Final test.

Final test

In this session you will pass the final test. After it we will summarize what you have learnt during the module.

Logarithms and their properties

In this session you will learn closer logarithms and their properties. You will get familiar with cases of using the properties of logarithms. algorithms

Functions

In this session you will recall the concept of function, and their roots. You will get familiar with discrete and continuous functions. You will calculate the roots of different functions.

Trigonometry

You will learn here the trigonometric functions, the relationships between them. You will also learn the formulas for transforming the trigonometric expressions.

Limits

In this session you will learn the concept of limit. You will learn standard methods to calculate limits.