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Calculus.......Anticipation. 360 B.C. Eudoxus of Cnidus rigorously developed Antiphon's method of exhaustion, close to the limiting concept of calculus which is used by himself and later the Greeks to find areas and volumes of curvilinear figures. 1600. Johannes Kepler
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360 B.C Eudoxus of Cnidus rigorously developed Antiphon's method of exhaustion, close to the limiting concept of calculus which is used by himself and later the Greeks to find areas and volumes of curvilinear figures. 1600 Johannes Kepler devised a method of finding the volumes of solids of revolution that (with hindsight!) can be seen as contributing to the development of calculus René Descartes inventor of the Cartesian coordinate system, the bridge between algebra and geometry, crucial to the discovery of infinitesimal calculus and analysis. Pierre de Fermat early developments that led to infinitesimal calculus. Discovery of an original method of finding the greatest and the smallest coordinates of curved lines, which is analogous to that of the then unknown differential calculus
Blaise Pascal work done by Fermat and Pascal into the calculus of probabilities laid important groundwork for Leibniz formulation of the infitesimal calculus Wallis contributed substantially to the origins of calculus and was the most influential English mathematician before Newton He studied the works of Kepler ,Cavalieri Robertval, Torricelli and Descartes, and then introduced ideas of the calculus going beyond that of these authors. He is also credited with introducing the symbol ∞ for infinity . He similarly used 1/∞ for an infinitesimal
Developing Newton Although calculus was the culmination of centuries of work rather than an instant epiphany, the two most recognized discoverers of calculus are Isaac Newton and Gottfried Wilhelm Leibniz. Newton went much further in exploring the applications of calculus .In 1715, just a year before Leibniz death, the Royal Society handed down their verdict crediting Sir Isaac Newton with the discovery of calculus. Newton's notation for differentiation, or dot notation, uses a dot placed over a function name to denote the time derivative of that function. While Newton did not have a standard notation for integration he wrote a small vertical bar above x to indicate the integral of x. He wrote two side-by-side vertical bars over x to indicate the integral of (x with a single bar over it). Another notation he used was to enclose the term in a rectangle to indicate its integral.
Leibniz He systematized Newton's ideas into a true calculus of infinitesimals. He now regarded as an independent inventor of and contributor to calculus. Leibniz mathematical notation has been widely used ever since it was published and still used to this day. Leibniz uses the symbols dxand dy to represent "infinitely small" (or infinitesimal) increments of x and y, just as Δx and Δy represent finite increments of x and y. Leibniz began using the character∫
1700 Joseph Louis Lagrange f'(x)for the first derivative, f''(x) for the second derivative, etc., were introduced by Lagrange (1736-1813). In 1772 Lagrange wrote the notation u' = du/dx and du = u'dx Legendre The "curly d" was used in 1770 by Nicolas de Condorcet However, the curly d was first used in the form ∂u/ ∂x by Legendre. Legendre abandoned the symbol and it was re-introduced by Jacobi n1841 1800 The arrow notation for limits. In the 1850s, Weierstrass began to use Our present day expression seems to have originated with the English mathematician John Gaston Leathem
Calculus Refined • From 19th century to the present Calculus has been refined and developed by many mathematicians. The fundamentals and notations developed by Newton and Leibniz are still seem widely today. • Some introductory textbooks still commemorate Leibniz and Newton. They typically credit Leibniz with integration and Newton with differentiation, though this is a simplification. The two men also live on through certain mathematical symbols. The modern integration symbol, for example, originated with Leibniz, as did the dy/dx notation for differentiation. Newton's own notation was a dot directly above the variable (read as "x-dot" or "y-dot"), and survives in many physics classrooms. • Few new branches of mathematics are the work of single individuals. Far less is the development of the calculus to be ascribed to one or two men.
