History of Mathematic Presentation/.pptx

M ATHEMATICS IN 17 TH AND 18 TH CENTURY

INTRODUCTION Hard on the heels of the “Copernican Revolution ” in the 16th Century, scientists in the 17th Century were making equally revolutionary discoveries . The invention of the logarithm in the early 17th Century by John Napier contributed to the advance of science, astronomy and mathematics. It was one of the most significant mathematical developments of the age, and 17th Century physicists like Kepler and Newton could never have performed the complex calculations needed for their innovations without it. This century also made significant contributions towards the development of calculus, as well as originating the idea of the number line, introducing the symbol “∞” for infinity and the term “continued fraction”, and extending the standard notation for powers to include negative integers and rational numbers. Moreover, this era is also credited on the discovery of the fundamental theorem of calculus, which essentially showed that integration and differentiation are inverse operations,and also made complete translations of Euclid into Latin and English.

FAMOUS MATHEMATICIANS IN 17TH CENTURY RENE DESCARTES PIERRE DE FERMAT BLAISE PASCAL ISAAC NEWTON GOTTFRIED W ILHEL M LEIBNIZ

REN É DESCARTES Is a french philosopher, mathematician, and scientist. Born in La Haye en Touraine, France on March 31, 1596 Father of Modern Philosophy Invented analytic geometry Devised rules for deductive reasoning Invented the cartesian Plane Developed the “rule of signs” technique Published the groundbreaking mathematical treatise “Discours de la method” (The Discourse on Method) Well known for his line cogito, ergo sum, (I think, therefore I am)

FAMOUS MATHEMATICIANS IN 17TH CENTURY RENE DESCARTES PIERRE DE FERMAT BLAISE PASCAL ISAAC NEWTON GOTTFRIED W I LHE L M LEIBNIZ

PIERRE DE FERMAT Is a French mathematician Born in Beaumont-de-lomagne, France Invented modern number theory Published the “Two Square Theorem” Known for his Fermat Numbers and conjuncture the “Last Theorem” were left unproven at his death. Developed the Method of Adequality and Analytic Geometry

FAMOUS MATHEMATICIANS IN 17TH CENTURY RENE DESCARTES PIERRE DE FERMAT BLAISE PASCAL ISAAC NEWTON GOTTFRIED W ILHEL M LEIBNIZ

BLAISE PASCAL He is best known for a convenient tabular presentation of binomial coefficients called “Pascal’s Triangle” that also help solve problems in probability Him together with Fermat have worked on “The Problem of Points” at its simplest can be illustrated by a simple game “winner take all”

FAMOUS MATHEMATICIANS IN 17TH CENTURY RENE DESCARTES PIERRE DE FERMAT BLAISE PASCAL ISAAC NEWTON GOTTFRIED W ILHEL M LEIBNIZ

ISAAC NEWTON He i s a n English polymath mathematician, physicist, astronomer, alchemist, theologian and philosopher. Born in Woolsthorpe, Lincolnshire, England Born on December 25, 1642 Died on March 20, 1727

ISAAC NEWTON He focused on the development of Calculus. He calculated a derivative function which gives a slope at any point of a function and the method is called "differential calculus" or "differentiation" He also formulated the inverse operation of differentiation called "Methods of Fluents" (now, integration or integral calculus) Despite of having known for contributing "calculus to mathematics discipline, he is also credited with the generalized binomial theorem which describes the algebraic expansion of powers of a binomial 5.

FAMOUS MATHEMATICIANS IN 17TH CENTURY RENE DESCARTES PIERRE DE FERMAT BLAISE PASCAL ISAAC NEWTON GOTTFRIED W ILHEL M LEIBNIZ

GOTTFRIED W ILHEL M LEIBNIZ He is an German polymath active mathematician , philosopher , physicist, and diplomat. Born in Leipzig, Germany Born on July 1, 1646 He died on November 14, 1716

GOTTFRIED W ILHEL M LEIBNIZ He developed a similar theory of calculus apparently completely independently . Within short period of two months, he had developed a complete theory of differential and integral calculus He discovered a method of arranging linear equations into an array called "Matrix, which could be manipulated to find a solution. He also worked on the invention of a practical calculating machine which used the binary system and was capable of multiplying, dividing and even extracting roots

NEWTON AND LEIBNIZ NOTATION Calculus Notation Differentiation Newton used a dot over the dependent variable to indicate a derivative, two dots for a second derivative, etc. Leibniz just used dx and dy to indicate infinitesimal increments in the independent and dependent variables. The use of the prime mark for derivatives dates from Joseph Louis Lagrange's work on differential calculus in the late 18th / early 19th Century. Integration Newton never used one consistent notation for integration, sometimes using a bar above a variable and sometimes putting the variable in a box. We have come to use Leibniz's notation, which uses an extended 'S' to indicate the sum of infinitely many infinitesimal quantities f(x) for each infinitesimal increment dx, between the two stated limits a and b.

Loga rithm Calculus Its discovery during 17th Century contributed significantly to the advance of mathematics. The logarithm of a number is the power or exponent by which another value must be raised to produce an equivalent value of the given number. Since its birth from 17th Century, it become one of the most important branches of mathematics that plays a major role in many scientific careers. Calculus is the mathematical study of change, in the same way that geometry is the study of shape, and algebra is the study of operations and their application to solving equations.

DELTA PROCESS Is the basic principle of differentiating or differentiation especially in algebraic polynomials. I

I I I N T R O D U C T I O N MATHEMATICS TEACHING IN 18TH CENTURY The period was dominated by one family, the Bernoulli's of Basel in Switzerland, which boasted two or three generations of exceptional mathematicians, particularly the brothers, Jacob and Johann. They were largely responsible for further developing Leibniz's infinitesimal calculus - particularly through the generalization and extension of calculus known as the "calculus of variations".

JACOB BERNOULLI Is a Swiss standard German mathematician He is also known as James in English and Jacques in French He was born in Basel, Switzerland on January 6, 1655 He died on August 16, 1705 He is one of the many prominent mathematicians in the Swiss Bernoulli family.

JOHANN BERNOULLI He is a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He was born in Basel, Switzerland in August 6, 1667 He died on January 1, 1748 He contributed significantly to the development of differential and integral calculus He is known for his contributions to infinitesimal calculus and educating Leonhard Euler in the pupil's youth.