Yes, the idea of differential and integral has existed since ancient times.

In the 3rd century BC, the ancient Greek mathematician and mechanic Archimedes (male

287 ~ 2 BC12) works "measurement of circles" and "on balls and circles"

The column already contains the seeds of calculus, and he is studying and solving parabolic problems.

The sum of the bow area under the line, the area of the ball and the crown, and the area under the spiral.

Modern integration is implicit in the volume problem of hyperbola of revolution.

Thought. As the basis of calculus, limit theory first appeared in China.

There are very detailed discussions in ancient times, such as Zhuang Zhou's Zhuang.

In the book "Zi", there is "a foot pestle, take it from the sky"

Half, inexhaustible. " The high emblem of the Three Kingdoms period was mentioned in his roundabout.

Fine cutting, little loss, too much cutting, no cutting.

Then it will fit the circle without losing anything. "He wrote" measuring cylinder "in 16 15.

In The New Science of Volume, a curve is regarded as an infinite increase in the number of sides.

A big straight line. The area of a circle is one of the areas of an infinite triangle.

Moreover, these can be regarded as the representative works of Huang Xian's thought. Italian figures

Cavalieri, a scientist, published "Geometry Necessary for Continuity" on 1635.

Think of a curve as an infinite number of line segments (non-components). this

All prepared for the birth of calculus later.

Newton's "Flow Count"

Another leap in the history of mathematics is the study of the change of "shape". 36860.8886888866 1

The development of productivity in 2 1 century has promoted the development of natural science and technology.

Not only the existing mathematical achievements have been further consolidated, enriched and expanded

Big, and because of the need of practice, began to study moving objects.

And then we can get the concept of variables and study the changes.

Generality of quantity and its correlation. To 17.

In the second half of this century, on the basis of previous creative research, Britain's great

Mathematician and physicist isaac newton from the perspective of physics.

When studying calculus, he created a kind of harmony in order to solve sports problems.

Newton called it "flow" as a mathematical theory of direct connection between physical concepts.

The theory of mathematics is actually the theory of calculus. Newton's has

The main works in charge of "flow calculation" are "Calculating the area of curved edge" and "Application"

Infinite polynomial equation and calculation method of flow and infinite pole number. this

These concepts are the mathematical reflection of the concept of force. Newton thought that any movement

Exists in space and depends on time, so he regards time as a change of self.

Quantity, the time-related strain as a flow, not only in this way, he

Geometrical figures-lines, surfaces and bodies-are also considered as knots of mechanical displacement.

Therefore, all variables are flow.

Newton pointed out that "flow counting" basically includes three types of problems:

(1) Know the relationship between flows and find the relationship between their flows.

Department, equivalent to differential calculus;

(2) Knowing the equation representing the flow number relationship, find the corresponding equation.

This is equivalent to integral, Newton's product.

Division includes not only finding the original function, but also solving the differential equation.

(3) The application scope of "flow counting" includes calculating the maximum value of the curve.

Value, minimum value, tangent and curvature of curve, length of curve and area of curved edge, etc.

Newton was fully aware of the above two kinds of problems (1) and (2).

It is a reciprocal operation, so the relationship between differential calculus and integral calculus is established.

Contact.

Newton mentioned 1665 in a manuscript on May 20th.

"Flow number", so some people regard this day as the symbol of the birth of calculus.

Leibniz made calculus more concise and accurate.

German mathematician Leibniz is independent from geometry.

Calculus was discovered at least several decades before Newton and Leibniz.

Mathematicians have studied it, and they started the birth of calculus.

But their work is fragmentary, incoherent and lacking.

Unity. Leibniz's Ways and Methods of Establishing Calculus and Newton

This is different. Leibniz is the tangent and curve of the curve studied.

Surrounding area, using analytical method to introduce the concept of calculus, get

Newton combined more in the application of calculus.

In kinematics, the attainments are higher than Leibniz's, but Leibniz's

Mathematical symbols are used in the form of expression, but they are far superior to Newton, who not only

Reveal the essence of calculus concisely and accurately, and promote it strongly.

The development of advanced mathematics is introduced.

The calculus symbols created by Leibniz are like India-A.

Rabe number promotes the development of arithmetic and algebra, and promotes the differential product.

Leibniz is the most outstanding symbol creation in the history of mathematics.

One of the creators.

Newton's differential and integral symbols are not used now.

The symbols used by Leibniz have been used to this day. Leibniz

I realized earlier and more clearly than others that good symbols can save a lot.

Thinking about labor and using symbolic skills is one of the keys to success in mathematics.