The Calculus Gallery: Masterpieces from Newton to Lebesgue

The Calculus Gallery: Masterpieces from Newton to Lebesgue

by William Dunham
     
 

ISBN-10: 0691136262

ISBN-13: 9780691136264

Pub. Date: 07/01/2008

Publisher: Princeton University Press

More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway into higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri

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Overview

More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway into higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth--mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. William Dunham lucidly presents the definitions, theorems, and proofs. "Students of literature read Shakespeare; students of music listen to Bach," he writes. But this tradition of studying the major works of the "masters" is, if not wholly absent, certainly uncommon in mathematics. This book seeks to redress that situation.

Like a great museum, The Calculus Gallery is filled with masterpieces, among which are Bernoulli's early attack upon the harmonic series (1689), Euler's brilliant approximation of pi (1779), Cauchy's classic proof of the fundamental theorem of calculus (1823), Weierstrass's mind-boggling counterexample (1872), and Baire's original "category theorem" (1899). Collectively, these selections document the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching--a story of genius triumphing over some of the toughest, most subtle problems imaginable.

Anyone who has studied and enjoyed calculus will discover in these pages the sheer excitement each mathematician must have felt when pushing into the unknown. In touring The Calculus Gallery, we can see how it all came to be.

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Product Details

ISBN-13:
9780691136264
Publisher:
Princeton University Press
Publication date:
07/01/2008
Edition description:
New Edition
Pages:
256
Sales rank:
472,253
Product dimensions:
6.00(w) x 9.10(h) x 0.70(d)

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Table of Contents


Illustrations ix

Acknowledgments xiii

INTRODUCTION 1

CHAPTER 1: Newton 5

CHAPTER 2: Leibniz 20

CHAPTER 3: The Bernoullis 35

CHAPTER 4: Euler 52

CHAPTER 5: First Interlude 69

CHAPTER 6: Cauchy 76

CHAPTER 7: Riemann 96

CHAPTER 8: Liouville 116

CHAPTER 9: Weierstrass 128

CHAPTER 10: Second Interlude 149

CHAPTER 11: Cantor 158

CHAPTER 12: Volterra 170

CHAPTER 13: Baire 183

CHAPTER 14: Lebesgue 200

Afterword 220

Notes 223

Index 233

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