Mathematical analysis, also known as advanced calculus, is the oldest and most basic branch of analysis. Generally speaking, it refers to a relatively complete mathematical subject with the general theory of calculus and infinite series as the main content, including their theoretical basis (basic theory of real number, function and limit). It is also a basic course for college mathematics majors.

The branch of analysis in mathematics is a branch of mathematics that specializes in studying real numbers and complex numbers and their functions. Its development began with calculus and extended to the continuity, differentiability and integrability of functions. These characteristics help us to study the material world and discover the laws of nature.

Early development:

In the early days of ancient Greek mathematics, the results of mathematical analysis were given implicitly. For example, Zhi Nuo's dichotomy paradox implies the sum of geometric series. Later, ancient Greek mathematicians such as eudoxus and Archimedes made the mathematical analysis more explicit, but it was not very formal.

When they calculate the area and volume of regions and solids by exhaustive method, they use the concepts of limit and convergence. In the early days of ancient Indian mathematics, Pashgaro, a mathematician in the12nd century, gave a second example of derivative.

Refer to the above content: Baidu Encyclopedia-Mathematical Analysis