/kloc-in the second half of the 0/7th century, European science and technology developed rapidly. Due to the improvement of productivity and the urgent needs of all aspects of society, through the efforts of scientists from all over the world and the accumulation of history, calculus theory based on function and limit concept came into being.
The idea of calculus can be traced back to the method of calculating area and volume proposed by Archimedes and others in Greece. Newton founded calculus in 1665, and Leibniz also published his works on calculus in 1673- 1676.
In the past, differential and integral were studied as two mathematical operations and two mathematical problems respectively. Cavalieri, Barrow, Wallis and others have obtained a series of important results of finding area (integral) and tangent slope (derivative), but these results are isolated and incoherent.
Only Leibniz and Newton really communicated integral and differential, and clearly found the internal direct relationship between them: differential and integral are two reciprocal operations. And this is the key to the establishment of calculus. Only by establishing this basic relationship can we establish systematic calculus. And from the differential and quadrature formulas of various functions, the algorithm program of * * * is summarized, which makes the calculus method universal and develops into a symbolic calculus algorithm. Therefore, calculus "was mostly done by Newton and Leibniz, not invented by them".
However, there has been a heated debate in the history of mathematics about the order in which calculus was founded. In fact, Newton's research on calculus was earlier than Leibniz's, but Leibniz's results were published earlier than Newton's.
Leibniz's paper "Finding a Wonderful Computing Type of Minimax" published in Teacher's Magazine on June 1684 is the earliest calculus document. This six-page paper is not rich in content and vague in reasoning, but it is of epoch-making significance.
Newton wrote in the first and second editions of Mathematical Principles of Natural Philosophy published three years later, namely 1687: "Ten years ago, in my correspondence with Leibniz, the most outstanding geometer, I indicated that I already knew the method of determining the maximum and minimum, the tangent method and similar methods, but I concealed this method in my correspondence ... The most outstanding scientist wrote back. He also described his method, which is almost no different from mine except for words and symbols "(but this passage was deleted in the third edition and later editions).
So it was later recognized that Newton and Leibniz created calculus independently.
Newton started from physics and studied calculus by set method. His application is more combined with kinematics, and his accomplishments are higher than Leibniz's. Leibniz, on the other hand, started from geometric problems, introduced the concept of calculus by analytical method, and got an algorithm, which was more rigorous and systematic than Newton's algorithm.
Leibniz realized that good mathematical symbols can save thinking labor, and the skill of using symbols is one of the keys to the success of mathematics. Therefore, the symbols of calculus he created are far superior to Newton's symbols, which has a great influence on the development of calculus. 17 13, Leibniz published the article "History and Origin of Calculus", summed up his thought of establishing calculus, and expounded the independence of his achievements.