Newton has recorded calculus in the manuscript of1May 20th, 665. In this manuscript, Newton introduced a letter with two points, which is equivalent to the homogeneous form of derivative. Therefore, some people regard this day as the glorious birth day of calculus. In fact, Newton's research on calculus began in the autumn of 1664, with kinematics as the background. This year, Newton had a clear understanding of calculus.

From the solstice in the summer of 1665 to the spring of 1667, Newton made a breakthrough in the study of calculus during his escape from the plague in his hometown. According to Newton's self-report, 1665+0 1 June, he invented the downstream counting method (differential method) and established the counter-current counting method (integral method) in May of the following year. In the month of 1666+00, Newton compiled the research results of the previous two years into a summary paper-A Brief Discussion on Flow Number, which is also the first systematic calculus document in history, marking the birth of calculus. In the next 20 years, Newton made unremitting efforts to improve and perfect his calculus theory, and successively completed three calculus papers: Analysis by Using Infinite Polynomial Equations (hereinafter referred to as Analysis, 1669) and Flow Method and Infinite Series (hereinafter referred to as Flow Method, 16765438+). They reflect the development process of Newton's calculus theory. However, Newton's paper on calculus was not published in time, and the public expression of his calculus theory first appeared in the book Mathematical Principles of Natural Philosophy published in 1687. Therefore, Principle has also become an epoch-making work in the history of mathematics.

Newton was very cautious about the publication of his scientific works. His most mature calculus book, Quadrature of Curves, was not published as an appendix to Optics until 1704. Later, other papers were published. Analytics was published after Newton's death.

After the appearance of calculus, the completeness of its operation and the universality of its application fully showed the power of this new mathematical tool, and calculus quickly became a powerful tool for studying natural science.