The calculus gallery : masterpieces from Newton to Lebesgue
Author(s)
Bibliographic Information
The calculus gallery : masterpieces from Newton to Lebesgue
Princeton University Press, c2005
Available at 13 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references and index
Description and Table of Contents
Description
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.
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
by "Nielsen BookData"