The Calculus Gallery: Masterpieces from Newton to Lebesgue

Description

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. 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