Calculus is a branch of mathematics, which studies the differential and integral of functions and related concepts and applications in higher mathematics. It is a basic subject of mathematics, including limit, differential calculus, integral calculus and its application. Differential calculus, including the calculation of derivatives, is a set of theories about the rate of change. It makes the function, velocity, acceleration and curve slope can be discussed with a set of universal symbols. Integral calculus, including the calculation of integral, provides a set of general methods for defining and calculating area and volume.

The main contents of differential calculus include: limit theory, derivative, differential and so on. The main contents of integral include definite integral, indefinite integral and so on. Generalized mathematical analysis includes calculus, function theory and many other branches, but now it is generally customary to equate mathematical analysis with calculus, and mathematical analysis has become synonymous with calculus. When it comes to mathematical analysis, you know that it refers to calculus.

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Calculus became a subject in the17th century, but the idea of integral appeared in ancient times.

The early history of integral calculus

In the 7th century BC, Thales, an ancient Greek scientist and philosopher, studied the area, volume and length of a ball, which included the idea of calculus. In the 3rd century BC, Archimedes (287 ~ 2 BC12 BC), an ancient Greek mathematician and mechanic, wrote Measurement of a Circle and Measurement on a Sphere and a Cylinder, which contained the seeds of integration. When he studied and solved the problems such as the arcuate area under parabola, the area under spiral and the volume obtained by rotating hyperbola, he implied the idea of modern integration.

China's ancient mathematicians also had the seeds of integral calculus, such as Liu Hui in the Three Kingdoms period. His thoughts on integral calculus mainly include two points: secant and volume.

Calculus generation

In the seventeenth century, there were many scientific problems to be solved, and these problems became the factors that prompted calculus. To sum up, there are mainly four kinds of problems: the first kind is the problem that appears directly when learning physical education, that is, the problem of finding the instantaneous speed. The second kind of problem is to find the tangent of the curve. The third kind of problem is to find the maximum and minimum of a function. The fourth problem is to find the length of the curve, the area enclosed by the curve, the volume enclosed by the surface, the center of gravity of the object, and the gravity of an object with a considerable volume acting on another object.

References:

Baidu Encyclopedia-Calculus (Mathematical Concept)