Calculus is a mathematical concept, which is a branch of higher mathematics that studies the differential and integral of functions and related concepts and applications. 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.

Since17th century, the concepts and skills of calculus have been continuously expanded and widely used to solve various practical problems in astronomy and physics, and great achievements have been made. But until19th century, in the development of calculus, the rigor of its mathematical analysis has not been solved.

In the eighteenth century, many great mathematicians, including Newton and Leibniz, realized this problem and tried to solve it, but they failed to solve it successfully.

Throughout the18th century, the foundation of calculus was confusing. Many British mathematicians may still be bound by the geometry of ancient Greece, so they doubt all the work of calculus.

This problem was not completely solved by French mathematician Cauchy until the second half of the19th century. Cauchy's limit existence criterion injects rigor into calculus and is the basis of limit theory. The establishment of limit theory makes calculus based on strict analysis, which also laid the foundation for the development of mathematics in the 20th century.

Geometric meaning:

Let Δ x be the increment of point m on the curve on the abscissa y=f(x), Δ y be the increment of the curve on point m corresponding to Δ x on the ordinate, and dy be the increment of the tangent of the curve on point m corresponding to Δ x on the ordinate. When | Δ x | is very small, |Δy-dy | is much smaller than |δx | (high-order infinitesimal), so we can use a tangent line segment to approximate the curve segment near point M.