The Calculus Gallery: Masterpieces from Newton to LebesguePrinceton University Press, 13 בנוב׳ 2018 - 256 עמודים 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. |
תוכן
| 1 | |
| 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 10 Second Interlude | 149 |
CHAPTER 11 Cantor | 158 |
CHAPTER 12 Volterra | 170 |
CHAPTER 13 Baire | 183 |
CHAPTER 14 Lebesgue | 200 |
Afterword | 220 |
Notes | 223 |
| 233 | |
מהדורות אחרות - הצג הכל
The Calculus Gallery: Masterpieces from Newton to Lebesgue <span dir=ltr>William Dunham</span> תצוגה מקדימה מוגבלת - 2018 |
The Calculus Gallery: Masterpieces from Newton to Lebesgue <span dir=ltr>William Dunham</span> תצוגה מקדימה מוגבלת - 2008 |
The Calculus Gallery: Masterpieces from Newton to Lebesgue <span dir=ltr>William Dunham</span> אין תצוגה מקדימה זמינה - 2005 |
מונחים וביטויים נפוצים
algebraic numbers analysis Augustin-Louis Cauchy Baire category theorem Bernoulli bounded category set Cauchy Cauchy’s chapter consider continuous functions curve defined definition dense set denumerable derivative differential calculus Dirichlet’s function discontinuous functions equation Euler example exists figure finite follows formula function f Georg Cantor graph Hankel’s harmonic series Henri Lebesgue Ibid ideas inequalities infinite series infinitely small integer coefficients intermediate value intuition irrational Jakob Johann Lebesgue integral Lebesgue’s Leibniz series lemma length Liouville mathematical mathematicians measure zero modern Newton notation nowhere-dense sets open interval Opera omnia original oscillation partition pathological function pointwise discontinuous pointwise limit polynomial proof proved quantities real numbers René Baire result Riemann integrable ruler function sequence ſº subinterval tion transcendental uniform convergence value theorem Vito Volterra Volterra Weierstrass whole number