First of all, their research contents are different:
1. Research content of mathematical analysis: research function, limit, calculus and series.
2. Research content of real variable function: The research content includes the continuity of real function, differential theory, integral theory and measure theory.
Second, they have different meanings:
1, the significance of mathematical analysis: the development of mathematical analysis 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.
2. Significance of real variable function: The further development of calculus is based on point set theory. The so-called point set theory is a theory that studies the properties of the set formed by points. It can also be said that the theory of real variable function is to study some basic concepts and properties in analytical mathematics on the basis of point set theory.
Third, the essence of the two is different:
1, the essence of mathematical analysis: analyzing the oldest and most basic branch. 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).
2. The essence of real variable function: the function with real number as independent variable is called real variable function, and the branch of mathematics with real variable function as the research object is called real variable function theory.
Baidu Encyclopedia-Real Variable Function (Mathematical Term)
Baidu Encyclopedia-Mathematical Analysis (Basic Branch of Mathematics)