More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway to 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. Now with a new preface by the author, this book documents 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, subtlest problems imaginable. In touring The Calculus Gallery, we can see how it all came to be.
William Dunham is a Research Associate in Mathematics at Bryn Mawr College. He is the author of Journey Through Genius: The Great Theorems of Mathematics, The Mathematical Universe, and Euler: The Master of Us All, and is a co-editor (along with Jerry Alexanderson and Don Albers) of The G.H. Hardy Reader. He received the Mathematical Association of America's George Polya, Trevor Evans, and Lester R. Ford awards, as well as its Beckenbach Prize for expository writing.
Author(s): William Dunham
Series: Princeton Science Library (Book 60)
Edition: New Princeton Science Library Edition
Publisher: Princeton University Press
Year: 2018
Language: English
Pages: 257
City: Princeton
Tags: Calculus, Analysis, History of Mathematics
Cover......Page 1
Title......Page 4
Copyright......Page 5
Dedication......Page 6
Contents......Page 8
Illustrations......Page 10
Acknowledgments......Page 14
Preface to the Princeton Science Library Edition......Page 16
INTRODUCTION......Page 22
CHAPTER 1 Newton......Page 26
CHAPTER 2 Leibniz......Page 41
CHAPTER 3 The Bernoullis......Page 56
CHAPTER 4 Euler......Page 73
CHAPTER 5 First Interlude......Page 90
CHAPTER 6 Cauchy......Page 97
CHAPTER 7 Riemann......Page 117
CHAPTER 8 Liouville......Page 137
CHAPTER 9 Weierstrass......Page 149
CHAPTER 10 Second Interlude......Page 170
CHAPTER 11 Cantor......Page 179
CHAPTER 12 Volterra......Page 191
CHAPTER 13 Baire......Page 204
CHAPTER 14 Lebesgue......Page 221
Afterword......Page 241
Notes......Page 244
Index......Page 254
