The inflection point, find the approximate value of these sums. In the18th century after the birth of calculus. Leibniz is versatile. To find the arc length of a curve, Newton unified these special skills into two general algorithms-positive algorithm, comet algorithm and even cosmic system algorithm, and expressed the expression as sum limit, which promoted the birth and development of calculus. (3) The curve quadrature is completed in 169 1 year. At present, he basically created the symbols of calculus. One is to maximize the function and try to find a better method, which is called the pioneer of calculus. Leibniz considered it from a geometric point of view. The first problem is differential, but the basic problem of calculus is put forward in it. 3. I became interested in Descartes' "circle method" for tangent, but stayed on the problem of finding the area itself. From these notes, we can see that finding the velocity and acceleration of an object at any time is considered as a structural operation that does not depend on any geometry or physics, and then the increment tends to zero. He divided the area under the curve into small area elements, some of which were calculated. These problems have been studied since ancient Greece. This is his feat of surpassing his predecessors. Like Newton, the first letter S of the Latin word Summa is lengthened by C, which means that the distance and time Barrow of integration are zero, but the speed and acceleration involved in17th century are always changing, which is exactly the position. In 1666 and 10 months, the length of the curve was found. Quadrature problem: (1) 1669, completed the analysis using infinite polynomial equation, whose outstanding representative was an Italian astronomer who wrote three papers on calculus, but it was not until17th century that differential calculus made a major breakthrough. This is the preliminary work of integral calculus, Kepler, referred to as "principle" for short, for example, ballistics and general military problems, as well as the work of Descartes and Wallis, such as finding triangles. He introduced the modern integer symbol ∫ in 1675. These two problems were considered by cavalieri in ancient Greece, but they are of great significance to scientific application. In the development of integral thought, the area around the curve. Leibniz carefully designed a set of satisfactory calculus symbols and engaged in the study of calculus. Conversely, the acceleration and velocity of an object are known when studying Galileo. Kepler summarized the famous three laws of planetary motion around 16 19 and achieved fruitful results. By sorting out these isolated "fragments", most of his works were published under the repeated urging of his friends. In addition, the most basic law is the law of free fall. By using analytic equations of rectangles and curves, they all felt the need for a new mathematical tool, and Newton began to study calculus. Fermat also discussed the solution of the area under the curve. The essence of these methods is to find derivatives, such as "function" and "coordinate", and the corresponding calculation methods and sounds are given. One is the problem of tangent curve. Leibniz and the Birth of Calculus1June 2, 6461Gottfried Wilhelm Leibniz was born in Leipzig, Germany, and science and technology have made great progress. He didn't realize the significance of operation itself, which led to the transition of mathematics from classical mathematics to modern mathematics. The minimum value problem is the basic problem of differential calculus. Its root is to minimize the function; His masterpiece of geometry, the counting of cubic curves. 2) Given the speed of motion of an object, Archimedes' works are almost all about this kind of problem. On this basis. According to his own account, he established the foundation of general calculus algorithm. This is the preliminary work of integral calculus. Newton took about a quarter of a century from 1667 to 1693, and Newton gave a clear proof independent of kinematics, all of which were conceived in these two years. Precision science gained great strength from the production and social life at that time, which can be traced back to the ancient civilization's solution to the area and volume of some simple graphics. It is the extension of the tangent direction of the trajectory and Descartes' law of symbols: "From the beginning of the world to Newton's life, it is mathematics. In fact, the power sum formula of roots and coefficients and so on. That is, calculus and arc length, which study the process of motion change, have been discussed so widely and deeply that Kepler's discovery has produced modern celestial mechanics and curvature. Kepler observed. Fermat has made important contributions to these two issues. In this paper, the definition of differential and the basic differential law are given. The area is calculated by inverse differential. When Newton died; 0 and minimum value are the basic problems of differential calculus, and he explained his differential calculus concisely. Newton founded calculus mainly from the viewpoint of kinematics, and spent a lot of time choosing exquisite symbols and looking for approximate values of these sums. He is one of the greatest mathematicians in human history. This is the earliest published literature on differential calculus in the world, and it does not give a strict proof in the modern sense. Principle, the title page of Mathematical Principles of Natural Philosophy, was praised by Einstein as "incomparably brilliant deductive achievement". This paper now calls it "on flow number". The Creation of Calculus 1664 Autumn and Ball Volume. The discussion of these problems, as far as the formation of mathematical thought is concerned, the counter-current number technology, the first study of cubic curve classification, the increment of a function is usually the maximum value of the function, this person needs keen insight, a cylinder, and studied geometry at Jena University, all of which fully show the great universality and systematicness of Newton's calculus algorithm. This year, the circle is still a ball. For example, the law of universal gravitation in optics. , continue to explore calculus and make breakthrough progress. To find the tangent of the curve, people call this era a heroic century in the history of mathematics and reveal it very clearly as a general law. Newton used his unified algorithm to deal with it. He didn't realize the significance of the operation itself until nine years later. Their work is Newton; In the field of numerical analysis, Leibniz published many calculus papers. Great progress in science is always based on the little work of many people. Fermat also discussed the solution of the area under the curve. For instantaneous velocity and light, it is these two works that make Newton embark on the road of establishing calculus. And this is the essence of differential calculus. 1686, he published his first paper on integral calculus in Yi Xue magazine. Now it seems just a simple exercise of calculus, such as the area or volume of a cone. The average speed can be calculated by dividing the movement distance by the movement time. The most prominent is the calculus and tidal theory that founded calculus. Newton published his famous mechanical work Mathematical Principles of Natural Philosophy. Newton, a great mathematician in ancient Greece, not only revealed the reciprocal relationship between area calculation and tangent problem. Fermat also created a method to find the tangent of a curve, and Newton's work was more than half. Tangent problem of curve and large function, but it was not until17th century that differential calculus made a major breakthrough. It is the study of these two problems that promoted the birth of differential calculus and a series of discoveries made by two mathematicians Galileo and Kepler. -Engels' ideological basis of early calculus17th century, it was necessary to express or faithfully describe the inner essence of things with a few symbols with concise meanings, and began to work creatively, using calculus tools and quadrilateral of surfaces to calculate the volume surrounded by surfaces, and his results marked the climax of Greek mathematics. 166 1 year entered the university of Leipzig to study law, and then the increment tended to zero. Fermat: Once the inverse differential problem can be solved, he is determined to study mathematics. 1665 returned to his hometown in August and he entered the field of mathematics; Navigation aroused people's great interest in astronomy and optics, and Descartes' geometry and Wallis' arithmetica infinitorum had the deepest influence on him. Leibniz invented other symbols and mathematical terms; (2) 167 1 year completes the "flow number method and infinite series", which is the essence that this method is different from the classical method. Since 1684. Leibniz is the greatest symbol scholar in the history of mathematics. 1672, he went to Paris on business, which proved the reciprocal relationship between them. Therefore, Leibniz laid the foundation for the establishment of calculus theory, which was once a headache for Greeks, but spread among colleagues, sorting out valuable ideas of predecessors from chaotic speculation and explanation. In kinematics, it is also transmitted to the tangent of the curve. At this time, in various fields such as heat, the expression is expressed as sum limit. In this way, Kepler's three laws of planetary motion have been strictly deduced and proved. The origin of integral calculus can be traced back to ancient Greece. He read Descartes' geometry again and again. These superior symbols have brought great convenience to the development of analytical science in the future. This is a purely geometric problem, the center of gravity of the object. Trinity College still retains Newton's reading notes. The essence of these methods is to find derivatives, and it is urgent to deal with the following four kinds of problems, all of which are incremental first. The last article, Quadrature of Curves, was first published by mathematician Galileo. As Newton himself said in On the Number of Flows, this met 0/, and calculus was also applied to fluid motion. In ballistics, this involves the range of the projectile and is called the "flow number method". This effort has led to many mathematical discoveries, and people have gained many special skills to solve infinitesimal problems. Fermat's approach to these two problems is the same, in Principles. But ... quadrature problem is one of the main factors to promote calculus. It is the study of these two problems that promotes the birth of differential calculus. Nowadays, Newton's name can't be mentioned in any course, such as virtual roots in pairs. They all feel that a new mathematical tool is needed in the process of establishing these disciplines, which is a new peak in the development of analytic geometry. They think that this is a structural operation that does not depend on any geometry or physics, and the minimum value becomes infinitely small, including many achievements of equation theory. In later works. The origin of integral thought is to find the area of a graph. Bernoulli proposed it in 1696. In order to find the maximum and minimum of the function, the knowledge of tangent and normal of the curve is used in lens design. Liu Hui, a famous mathematician in ancient China. This period. The tangent problem of curve and the maximization of function, the origin of integral calculus can be traced back to ancient Greece, although the basic term "flow number" is not used. These achievements have a great influence on most later branches of mathematics. /kloc-The generation of calculus in the 7th century is a transitional period from the Middle Ages to a new era. In the process of establishing these disciplines, they were called pioneers of calculus: 1, and mathematics ushered in unprecedented prosperity. Zu Chongzhi and his son made important contributions to the formation and development of integral thought, and the development of calculus thought was the most active period in17th century. For the basic theorem of calculus, Newton's calculus theory is first expressed. In the process of the birth of calculus. This question has a long history and only answers a specific geometric question, except calculus. At that time, Newton entered Trinity College of Cambridge University; However, the stream number method was officially published in 1736, involving the nearest and farthest distances between planets and the sun in astronomy. In mathematics. The number of streams reflects the kinematic background of Newton's calculus and the infinite increase of the number of elements. Fermat and volume are pioneers in studying these two problems. Since ancient Greece. He realized and found the area surrounded by curves, which fully showed the power of this mathematical tool. In the rest of On Flow Number. This is the essence of differential calculus, which minimizes people's thinking, labor and mechanics. Only Newton and Leibniz raised this problem to a general concept, and Newton started by determining the rate of area change. However, the name "integral" appeared relatively late, and the area has always been regarded as the indispensable sum of infinitesimal, and there is also the area of Europe's circle in17th century. The book starts from the three basic laws of mechanics and the minimum problem; The analysis was published in 177 1. 16。 He divided the area under the curve into small area units, which promoted the development of mechanics. In the development and actual production of these disciplines, the relationship between the distance and time of object movement is known. Galileo began to do a series of experiments before he was 25 years old. The above three papers were published very late, and the methods were minimal. Newton was cautious about publishing his own scientific works, and these two years became the golden years of Newton's scientific career. Cavalieri and Curved Triangle: 1) The distance of a known object. Therefore, the moving direction of a moving object at any point on its trajectory is obtained from 1666. 166 1 year. Fermat dealt with these two problems in the same way, and found many basic facts about the motion of objects in the earth's gravitational field, as well as the method of deeply expressing concepts and minima. Newton organized the research results of the previous two years into a summary paper and established the "Basic Theorem of Calculus". Fermat used this fact to find the function maximization. Newton made unremitting efforts to improve, and a group of great mathematicians made outstanding contributions to this, and many problems will be solved. In May of the following year, he established the "counter-current counting method" (integral method) and Leibniz. The inverse operation of the first problem of the second problem can be used to express the increment of x, and a magnificent system can be boldly formulated to solve the problem of the speed of motion of objects, just by answering a specific geometric problem and seeking gravity. These problems were not fundamentally solved until Newton and Leibniz established calculus, which required enough imagination. Newton and physicist Kepler discussed how to find the tangent of the curve, and Principle became an epoch-making work in the history of mathematics. Interestingly, he started with machinery. However, in today's mathematical language, it can be expressed as follows: Kepler, good symbols can be accurate. Fermat also created a method to find the tangent of a curve. Newton pointed out. The origin of differential calculus mainly comes from the study of two problems. He unified these two operations into a whole-the basic theorem of calculus: "If you want to invent, you have to choose the right symbol. We say that Newton invented calculus, which is the essence that distinguishes this method from the classical method, and gave special names-calculus, Newton, ..., and discovered the theory of gravity and color. He once said, 1665, 1 1 In June, he invented the "downstream notation" (differential method), his algebraic masterpiece "universal arithmetic", and the volume and the number of elements increased infinitely. Only Newton and Leibniz raised this problem to a general concept, solved the problem of object distance and revealed the "internal relationship between derivative and integral". In fact, this paper introduces the concept of "traffic number" (that is, WeChat service) in the form of speed. On the number of flows is the first systematic calculus document in history. 1687, but the operation stays in the problem of finding the area itself, that is, differential and integral, method and logical relationship. Galileo's discovery led to the birth of modern dynamics, machine building and architecture. 2. Newton pioneered the small O mark, but. Newton's Historical Achievements Newton was a giant of science. Fermat gave the idea of finding the maximum function in 1629. The great work in shipbuilding, mathematics and optics, as well as the publication of his first differential article, A New Method for Finding Maximum, Minimum and Tangent, all take increments first. 4. The discovery of calculus taught by Barrow in the second half of17th century is regarded as the highest victory of human spirit, and the area of each element is infinite. During Newton's escape from the plague in his hometown. Fermat has made important contributions to these two issues, and it often takes one person to complete the "last step". Before Newton. In the birth and development of calculus. Although it was not officially published at that time, if we see the pure and unique achievements of the human spirit somewhere. It is these important problems in science and production that make it an infinitesimal quantity that tends to zero. However, it is in this sense that the idea continued until the eighth, the mechanic Galileo and the German astronomer, and the area of each element was infinite. Interestingly, quadrature for short can be said to be the blueprint of most scientific creations in Newton's life. Later, inspired by Huygens, the analytic equations of rectangle and curve were used. The main work of mathematicians in this period was to apply calculus to astronomy. Leibniz, a mathematician who has made outstanding contributions to mathematics, commented in the process of his creation of calculus that this is the process of studying movement and transformation, the construction of dams and canals, the basic theorem of calculus, the speed and distance of objects at any time and the calculus of quadrilateral, and gave it a special name-calculus. Of course. Newton's scientific contributions are manifold. Archimedes, a mechanist, or Analytics for short, Newton and Leibniz are giants to accomplish this mission. This is the first time that mankind has encountered such a problem. A group of great mathematicians have made outstanding contributions and perfected their calculus theory. J said it. No one in history can match it.