## CalculusBy Daniel Rubio and Adriano Bernal.

### Newton

Newton:

Newton was not very intelligent at school he dropped out one time and the other time he went to Cambridge where he graduated but he failed the last exam.

"He then further theorized that the rate of the apple's fall was directly proportional to the attractive force which the Earth exerted upon it. In addition, he suggested the inverse square law; force decreases according to the square of the distance from the center of the Earth".

"In the Principia MathematicaPrincipia Mathematica, which appeared in 1687, Newton arranged Galileo's findings into three basic laws of motion : a body at rest remains at rest, and a body in motion remains in motion; force is equal to mass times acceleration; for every action, there is an equal and opposite reaction. These three laws allowed Newton to calculate the gravitational force between the Earth and the moon. He asserted these laws acted upon any two objects in the universe, establishing the law of universal gravitation, and proceeded to estimate, quite accurately, the masses of Jupiter and Saturn".

Newton had a rivalry with Gottfried Wilhelm Leibniz he even demanded Leibniz and send him to court.

G. (Ed.). (n.d.). Isaac Newton. Retrieved March 30, 2017.

### Leibniz

"Leibniz particularly wished to reduce the tedium of astronomy and navigational calculations and believed that a mechanical calculating device could be the solution. After studying Blaise Pascal's calculator, he realized that he could improve upon its design to perform multiplication and division--functions that Pascal's device could not do. In 1671 he introduced his calculator, but could not fully develop the calculator's design until three years later. Multiplication and division were accomplished by the repetition of the addition and subtraction functions on the machine".

"In addition to his calculator, Leibniz achieved great success in mathematics and science. As early as 1666, he published his first paper on mathematics. Entitled De arte combinatorica, this paper represented Leibniz's belief that the logic of thought could be reduced to mathematical calculations--concepts put to use years later in development of Boolean algebra and digital computer design".

"In the years following his studies in symbolic logic, Leibniz focused his genius toward developing a system of differential and integral calculus. In 1675 he wrote an unpublished manuscript that gave the product rule for differentiation and that also used for the first time our familiar integral notation. Leibnitz finally published the fundamental concepts of his differential calculus in 1684, including his notation for differentiation using dx and dy, and the rules for computing the derivatives of powers, products and quotients. Two years later he published a paper dealing with the integral calculus in which he emphasized the inverse relationship between differentiation and integration as a summation process, one of the fundamental theorems of calculus. Although Isaac Newton had already done similar work some years earlier, Leibniz's notation was considered superior and came to be preferred over that of Newton. A bitter controversy developed between Newton and Leibniz, and between their supporters, concerning the independence and priority of the discovery of calculus. Today mathematicians recognize both for their fundamental contributions".

"Unfortunately, by the time of his death in 1716, many in the scientific and mathematical communities had already forgotten him; the only mourner at his funeral was his secretary".

G. (Ed.). (n.d.). Gottfried Wilhelm Leibniz. Retrieved March 30, 2017.

#### FACTS

Gottfried Wilhelm Leibniz (1646–1716), a German philosopher and mathematician, created a machine in 1671 which did addition and multiplication. For over 200 years this machine was lost; then it was discovered by some workmen in the attic of one of the Göttingen University's buildings.

After studying the earlier calculator of French mathematician Blaise Pascal (1623-1662), Leibniz realized that he could improve upon its design to perform multiplication and division--Pascal's machine could only add and subtract. In 1671, he introduced his calculator, which became quite a success. After demonstrating it for the Royal Society in London in 1673, they elected him a member of the scientific organization. His innovations on the calculator included the use of multiplier wheels and a delay carry mechanism

G. (Ed.). (n.d.). CALCULATOR. Retrieved March 31, 2017.

#### Calculus

Newton:

Calculus marks the beginnings of what is called higher mathematics. Its invention provided mathematicians and scientists with a powerful tool to solve problems that had been unsolvable before. A typical problem that can only be solved by calculus involves a relationship that is 1) both dynamic or rapidly changing and 2) also affected by many different factors (like time, speed, distance, force) at the same time. Most historians now agree that Newton and Leibniz each invented their own versions of calculus independent of the other, with Newton doing it first by eight to ten years. However, since Newton was typically very late in publishing his work, the publications of Leibniz in 1684 and 1686 were first.

Newton's law of universal gravitation states that any two objects in the universe attract one another with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Basically, the larger the object, the greater the gravitational force it exerts. The closer the objects, the greater the gravitational attraction between them. This worked very well to explain the motion of the planets in the solar system. Newtonian physics held sway for over 200 years, until German-born American physicist Albert Einstein (1879-1955) published his general theory of relativity in 1916.

G. (Ed.). (n.d.). Isaac Newton. Retrieved March 31, 2017.

Jacobo Bernoulli

En 1690 se convirtió en la primera persona en desarrollar la técnica para resolver ecuaciones diferenciales separables.

Muy cercano a Leibniz y por ello empezo a adoptar el calculo, hasta que aparecio los procesos matematicos que usaban no tenían nombre, Jacobo los nombro calculo y ese es el nombre que se usa incluso hoy en día.

Falleció a los 50 años por culpa de la tuberculosis, ocho años despues su sobrino publico su obra maestra, un trabajo sobre la teoría de la probabilidad.

Jakob Bernoulli. (2017, April 02). Retrieved March 31, 2017, from https://es.wikipedia.org/wiki/Jakob_Bernoulli

#### Obras de Newton y Leibniz

Entre 1665 y 1666 Newton escribió varias obras pero nunca las publico por miedo a que se las robaran.

Entre ellas la ley del inverso del cuadrado de la distancia en la gravitación, su desarrollo de las bases de la mecánica clásica, la formalización del método de fluxiones y la generalización del teorema del binomio.

Newton había descubierto los principios de su cálculo diferencial e integral hacia 1665-1666 y, durante el decenio siguiente, elaboró al menos tres enfoques diferentes de su nuevo análisis.

Newton y Leibniz protagonizaron una agria polémica sobre la autoría del desarrollo de esta rama de la matemática. Ya que los dos desarrollaron el calculo por separado, igualmente los dos se intercambiaban resultados.

En un 11 de noviembre de 1675 Leibniz demuestra el cálculo de una integrada por primera vez bajo el grafismo y = ƒ(x).

11 de noviembre. (2017, March 28). Retrieved April 01, 2017, from https://es.wikipedia.org/wiki/11_de_noviembre

Isaac Newton. (2017, April 02). Retrieved April 01, 2017, from https://es.wikipedia.org/wiki/Isaac_Newton

Credits:

Created with images by Pexels - "abacus calculus classroom" • Cea. - "Time" • bazzadarambler - "Oxford University Museum of Natural History ... Sir Isaac Newton contemplates a fallen apple." • Stifts- och landsbiblioteket i Skara - "Godefridvs Gvilielmvs L B de Leibniz" • STA82 - "calculator graphing calculator casio fx-7000 g" • Skakerman - "Calculus III"

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