The Calculus Gallery: Masterpieces from Newton to Lebesgue - download pdf or read online

By William Dunham

More than 3 centuries after its construction, calculus continues to be a stunning highbrow fulfillment and the gateway into better arithmetic. This e-book charts its development and improvement by means of sampling from the paintings of a few of its superior practitioners, starting with Isaac Newton and Gottfried Wilhelm Leibniz within the past due 17th century and carrying on with to Henri Lebesgue on the sunrise of the twentieth--mathematicians whose achievements are akin to these of Bach in tune or Shakespeare in literature. William Dunham lucidly offers the definitions, theorems, and proofs. "Students of literature learn Shakespeare; scholars of song take heed to Bach," he writes. yet this practice of learning the key works of the "masters" is, if now not totally absent, definitely unusual in arithmetic. This publication seeks to redress that situation.

Like an excellent museum, The Calculus Gallery is full of masterpieces, between that are Bernoulli's early assault upon the harmonic sequence (1689), Euler's awesome approximation of pi (1779), Cauchy's vintage evidence of the elemental theorem of calculus (1823), Weierstrass's mind-boggling counterexample (1872), and Baire's unique "category theorem" (1899). jointly, those decisions record the evolution of calculus from a strong yet logically chaotic topic into one whose foundations are thorough, rigorous, and unflinching--a tale of genius winning over the various hardest, so much refined difficulties imaginable.

Anyone who has studied and loved calculus will notice in those pages the sheer pleasure every one mathematician should have felt whilst pushing into the unknown. In traveling The Calculus Gallery, we will see the way it all got here to be.

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The Calculus Gallery: Masterpieces from Newton to Lebesgue by William Dunham

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