The calculus of newton

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  • The discovery of infinite products byWallis and infinite series by Newton marked the beginning of the modern mathematical era. The use of series allowed Newton to find the area under a curve defined by any algebraic equation, an achievement completely beyond the earlier methods ofTorricelli, Fermat, and Pascal. The work of Newton and his contemporaries, including Leibniz and the Bernoullis, was concentrated in mathematical analysis and physics.

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  • The art of teaching, Mark Van Doren said, is the art of assisting discovery. I have tried to write a book that assists students in discovering calculus—both for its practical power and its surprising beauty. In this edition, as in the first five editions, I aim to convey to the student a sense of the utility of calculus and develop technical competence, but I also strive to give some appreciation for the intrinsic beauty of the subject. Newton undoubtedly experienced a sense of triumph when he made his great discoveries. I want students to share some of that excitement.

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  • Ato Z of Mathematicians contains the fascinating biographies of 150 mathematicians: men and women from a variety of cultures, time periods, and socioeconomic backgrounds, all of whom have substantially influenced the history of mathematics. Some made numerous discoveries during a lifetime of creative work; others made a single contribution. The great Carl Gauss (1777–1855) developed the statistical method of least squares and discovered countless theorems in algebra, geometry, and analysis.

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  • At the time of Isaac Newton’s invention of the calculus in the 17th century, the mechanical clock was the most sophisticated machine known. The simplicity of the clock allowed its movements to be completely described with mathematics. Newton not only described the clock’s movements with mathematics, but also the movements of the planets and other astronomical bodies. Because of the success of the Newtonian method, a mathematics-based model of reality resulted.

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  • Important breakthroughs in the foundations of mechanical engineering occurred in England during the 17th century when Sir Isaac Newton both formulated the three Newton's Laws of Motion and developed Calculus, the mathematical basis of physics. Newton was reluctant to publish his methods and laws for years, but he was finally persuaded to do so by his colleagues, such as Sir Edmund Halley, much to the benefit of all mankind.

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  • IT HAS BEEN SAID THAT SIR ISAAC NEWTON was the last person to know everything. He was an accomplished physicist (his three laws of motion were the basis of classical mechanics, which defi ned astrophysics for three centuries), mathematician (he was one of the inventors of calculus and developed Newton’s Method for fi nding roots of equations), astronomer, natural philosopher, and alchemist (okay, maybe the last one was a mistake). He invented the refl ecting telescope, a theory of color, and a law of cooling, and he studied the speed of sound.

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