The main content of mathematical analysis is calculus. The theoretical basis of calculus is limit theory, and the theoretical basis of limit theory is real number theory. 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 research object of mathematical analysis of extended data is function, and the basic form of function is studied from both local and whole aspects, thus forming the basic content of differential calculus and integral calculus. Differential calculus studies the local characteristics of functions, such as the rate of change. Derivative and differential are its main concepts, and the process of finding derivative is differential method. Around the nature, calculation and direct application of derivative and differential, the main content of differential calculus is formed.

Integral studies the total effect of small changes (especially non-uniform changes) as a whole. Its basic concepts are original function (anti-derivative) and definite integral, and the process of finding integral is integral method.

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