1, Introduction: The mathematical concept of calculus 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.
2. Theory: 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.
3. Early history: In the 7th century BC, Thales, an ancient Greek scientist, studied the area, volume and length of the ball, which included the idea of calculus. In the 3rd century BC, Archimedes, an ancient Greek mathematician and mechanic, already contained the seeds of integration in his books "Measurement of Circle" and "On Sphere and Cylinder". When he studied and solved the problems of arch area under parabola, spherical cap area, spiral area and volume calculation by rotating hyperbola, he implied the idea of modern integration.