History of Mathematical Analysis
Mathematical analysis is a system of disciplines that are united by the following characteristics. These disciplines mainly study the quantitative relations of the real world (in contrast to the geometrical disciplines dealing with its spatial properties). Here there is a slight similarity with arithmetic, since the relations themselves are expressed by means of numerical quantities. But arithmetic (and algebra) deals mainly with constant quantities (which characterize states), while in mathematical analysis variable quantities characterize the processes themselves. The basic concepts of analysis are the function and the limit, with the help of their various properties and further study.

Many sections of mathematical analysis now exist as separate subjects, such as differential equations, functional analysis. Now the main sections of analysis would be: differential calculus, integral calculus, and series theory.

The rudiments of the methods of mathematical analysis were used by the ancient Greek mathematician Archimedes. But already in the 17th century, these methods had been systematized and received a new impetus to development. And at the turn of XVII and XVIII centuries the great English mathematician and physicist J. Newton and the famous German philosopher and mathematician H. W. Leibniz, completed the basic sections of mathematical analysis: differential and integral calculus, and laid the foundation of the doctrine of series and differential equations. In the 18th century, L. Euler, who did much for the development of mathematics and worked in several states, developed the last two sections and laid the foundation for other disciplines of mathematical analysis.

And so by the end of the 18th century a huge amount of factual material had accumulated, but it was insufficiently developed logically. This deficiency was remedied by the efforts of the largest scientists of the nineteenth century, such as O. L. Cauchy] in France, N. H. Abel in Norway, H. F. B. Riemann in Germany, and others. Who brought more than one theorem, which is now often used in teaching mathematical analysis.