Mathematical analysis is a basic course for mathematics majors. Learning mathematical analysis (and advanced algebra) well is the necessary basis for learning other subsequent mathematics courses such as differential geometry, differential equations, complex variable functions, real variable functions and functional analysis, calculation methods, probability theory and mathematical statistics.

Mathematical analysis is one of the compulsory courses for mathematics majors, and its basic content is calculus, but it is quite different from calculus. Calculus is a general term for differential calculus and integral calculus, which is abbreviated as calculation in English, because early calculus was mainly used for calculation problems in astronomy, mechanics and geometry. Later, people also called calculus analysis, or infinitesimal analysis, especially the knowledge of using extreme processes such as infinitesimal or infinity to analyze and deal with calculation problems. The early calculus was not developed for a long time because it could not convincingly explain the concept of infinitesimal. Cauchy and later Wilstrass perfected the limit theory as the theoretical basis, which made calculus gradually evolve into a basic mathematical discipline with strict logic, called "mathematical analysis" and translated into Chinese as "mathematical analysis".