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 calculus has been used by mathematicians and astronomers to solve a large number of practical problems, but it has not been developed for a long time because it cannot give a convincing explanation for the concept of infinitesimal. Many mathematicians are skeptical about this theory, and Cauchy and later Wilstrass perfected the limit theory as the theoretical basis.
Get rid of the vague description of limit, such as "the smaller the better" and "infinite tendency", and use accurate mathematical language to describe the definition of limit, so that calculus gradually evolves into a basic mathematical discipline with strict logic, called "mathematical analysis", which is translated into Chinese.