Calculus, the basic part of these problems, is a branch of mathematics that 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 basic concepts and contents of calculus include differential calculus and integral calculus. 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.
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.