In 1686, Newton published the first paper on integrals
Calculus (mathematical concepts):...
... Differentiation, differentiation: see Newton 321~336...
... Products, points, points: see Newton 337~405...
... Calculus: See Newton 407...
... Mathematics, Learning, Mathematics: See Euclid 49...
(...Euclid: Novel title... ）
... Concepts, Concepts: See Euclid 22, 23...
Calculus history
... History, History: See Euclid 111...
... History of Calculus: See Newton 407, 408...
…
In the second half of the seventeenth century, on the basis of the work of previous generations, the Great British scientist Newton and the German mathematician Cí studied and completed the creation of calculus on their own in their own countries, although this was only a very preliminary work.
... Work, Work, Work: See Galileo 22...
(...Galileo: Novel title... ）
... Basis, Foundation, Foundation: See Euclid 37...
... Science, Learning, Science: See Euclid 4...
... Home: A person who has mastered a certain specialized knowledge or engaged in a certain specialized activity: specialized~ Draw ~. Politics~. Science~. Art~. Social Activities ~... See Euclid 92...
... Leibniz: See Euclid 131...
... Research, research, research: see Euclid 42...
Their greatest achievement (Newton and Leibniz) was to link two seemingly unrelated problems, one with tangentials (the central problem of differential calculus) and the other with the problem of product (the central problem of integrals).
... Question, question, question: See Galileo 76...
... Connections, Departments, Connections: See Euclid 149...
... Cut, line, tangent: see Newton 288...
Newton and Leibniz established calculus from the point of view of intuitive infinitesimals, so the discipline was also called infinitesimal analysis in the early days, which is the origin of the name of the large branch of analytics in mathematics today.
... Intuitive: See Newton 220...
... Nothing, Poor, Infinite, Small, Infinitesimal: See Newton 280...
... Volume: See Euclid 27...
... Division, analysis, analysis: see Euclid 36...
Newton's study of calculus focused on kinematics, while Leibniz focused on geometry.
... Movement, Movement, Movement, Learning, Kinematics: See Galileo 37...
... Geometry: see Euclid 28...
Newton's development
... Development, Development: See Galileo 21...
Newton wrote Flow Numbers and Infinite Series in 1671, a book that was not published until 1736.
... Series: Also called infinite series... See Galileo 57...
In this book, he pointed out that variables are produced by the continuous motion of points, lines, and surfaces, and negated his previous belief that variables were static sets of infinitesimal elements.
... Variables, quantities, variables: see Euclid 29...
... Continuous, continuous, continuous: see Euclid 44...
... Movement, Movement: See Galileo 9...
... Elements, Elements: See Euclid 45...
... Collections, Collections: See Euclid 31...
He (Newton) called the continuous variables the flow quantities and the derivatives of these flow quantities the flow numbers.
... Derivatives, numbers, derivatives: see Newton 288~294...
The central problem posed by Newton in flow numbers is the known path of continuous motion, the velocity of a given moment (differential method); the known velocity of motion, the distance traveled in a given time (integral method).
... Spell: See Euclid 29...
... Speed, degree, speed: see Galileo 3...
... Time, Time, Time: See Galileo 10...
Leibniz
Leibniz of Germany was a polymath who, in 1684, published what is now considered to be the earliest calculus literature in the world, which has a long and outlandish name—"A New Method for Finding Maximal Minimums and Tangents, Which Also Applies to Fractions and Irrational Quantities, and to The Wonderful Types of Computation of This New Method."
... World, World, World: See Euclid 110...
... Fang, Method, Method: See Euclid 2, 3...
... Counting, counting, calculating: see Euclid 157...
It is such a reasoned and pō-vague article, but it has epoch-making significance. It already contains modern differential symbols and basic differential laws.
... Meaning, righteousness, meaning: see Euclid 26...
... Symbols, symbols: see Euclid 160, 161...
... Base, Ben, Basic: See Euclid 2...
... Law, Rule, Law: See Euclid 108...
In 1686, Leibniz published the first literature on integrals.
Leibniz is one of the greatest semioticians in history, and the calculus symbols he created were far superior to Newton's symbols, which had a great influence on the development of calculus.
The calculus common notation we use today was carefully chosen by Leibniz at that time.
For Newton used the geometric method in his major work on calculus and in his first publication, The Mathematical Principles of Natural Philosophy. So for more than a hundred years after Newton's death, the British continued to use geometry as their main tool.
And continental mathematicians continued Leibniz's method of analysis, allowing it to develop and improve.
The impact of these events was enormous, not only leaving British mathematicians behind, but also costing mathematics some of the most talented people, through the application of calculus, the contributions they could make.
See the next episode, "Newton 410, The Struggle over Calculus Priority, Brings Mathematicians in Britain and Continental Europe to a Halt to the Exchange of Ideas."
If you don't know history, you can't see the future
Welcome to the headline "The Game of Human Nature"