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.

zlib/Mathematics/Others/[美]William Dunham/微积分的历程：从牛顿到勒贝格 (图灵新知)_17250142.azw3

微积分的历程 : 从牛顿到勒贝格 = The calculus gallery : masterpieces from Newton to Lebesgue

邓纳姆 (Dunham, William)

邓纳姆; 李伯民; 汪军; 张怀勇

美 William Dunham

WilliamDunham著

The People's Posts and Telecommunications Publishing House

Princeton University, Department of Art & Archaeology

Princeton University Press

Tu ling xin zhi xi lie tu shu, Di 1 ban, Beijing, 2010

Princeton University Press, Princeton, N.J., 2008

Tu ling xin zhi, Di 1 ban, Beijing Shi, 2010

United States, United States of America

China, People's Republic, China

图灵新知, Di 1 ban, Beijing, 2010

Princeton, N.J, ©2005

Princeton [u.a, 2008

6.1.2008, 2008

May 6, 2008

Bookmarks: p1 (p1): 前言
p2 (p7): 第1章 牛顿
p3 (p8): 广义二项展开式
p4 (p11): 逆级数
p5 (p14): 《分析学》中求面积的法则
p6 (p18): 牛顿的正弦级数推导
p7 (p22): 参考文献
p8 (p24): 第2章　莱布尼茨
p9 (p27): 变换定理
p10 (p35): 莱布尼茨级数
p11 (p40): 参考文献
p12 (p41): 第3章　伯努利兄弟
p13 (p43): 雅各布和调和级数
p14 (p47): 雅各布和他的垛积级数
p15 (p52): 约翰和Xx
p16 (p57): 参考文献
p17 (p59): 第4章 欧拉
p18 (p60): 欧拉的一个微分
p19 (p62): 欧拉的一个积分
p20 (p63): π的欧拉估值
p21 (p67): 引人注目的求和
p22 (p72): 伽玛函数
p23 (p76): 参考文献
p24 (p78): 第5章　第一次波折
p25 (p86): 参考文献
p26 (p87): 第6章　柯西
p27 (p88): 极限、连续性和导数
p28 (p91): 介值定理
p29 (p94): 中值定理
p30 (p97): 积分和微积分基本定理
p31 (p102): 两个收敛判别法
p32 (p107): 参考文献
p33 (p109): 第7章　黎曼
p34 (p112): 狄利克雷函数
p35 (p114): 黎曼积分
p36 (p121): 黎曼病态函数
p37 (p126): 黎曼重排定理
p38 (p129): 参考文献
p39 (p131): 第8章　刘维尔
p40 (p132): 代数数与超越数
p41 (p136): 刘维尔不等式
p42 (p141): 刘维尔超越数
p43 (p145): 参考文献
p44 (p146): 第9章　魏尔斯特拉斯
p45 (p148): 回到基本问题
p46 (p158): 四个重要定理
p47 (p160): 魏尔斯特拉斯病态函数
p48 (p170): 参考文献
p49 (p171): 第10章　第二次波折
p50 (p181): 参考文献
p51 (p182): 第11章　康托尔
p52 (p183): 实数的完备性
p53 (p186): 区间的不可数性
p54 (p190): 再论超越数的存在
p55 (p195): 参考文献
p56 (p196): 第12章　沃尔泰拉
p57 (p198): 沃尔泰拉病态函数
p58 (p200): 汉克尔的函数分类
p59 (p204): 病态函数的限度
p60 (p210): 参考文献
p61 (p211): 第13章　贝尔
p62 (p212): 无处稠密集
p63 (p215): 贝尔分类定理
p64 (p219): 若干应用
p65 (p225): 贝尔的函数分类
p66 (p228): 参考文献
p67 (p230): 第14章　勒贝格
p68 (p231): 回归黎曼积分
p69 (p232): 零测度
p70 (p239): 集合的测度
p71 (p243): 勒贝格积分
p72 (p250): 参考文献
p73 (p252): 后记

<p><P>"<i>The Calculus Gallery</i> is one of the best efforts at mathematical exposition I have ever read! Dunham presents in detail and in his own words the sequence of ideas of classical giants of mathematics, but each new idea is described in modern terms and notation, so I had absolutely no trouble following along. Furthermore&#151;and this is an astounding achievement&#151;the entire work has a tightly woven development. If it were a detective story I would say it had a plot with no loose ends. An amazing feat. I wish I could plan a single lecture, never mind a course or a book, that well!"&#151;Henry Pollak, Teachers College, Columbia University<P>"What a fine resource! All of the famous functions that have shaped calculus and analysis parade before the reader in the original words of their creators. Bill Dunham has produced an excellent volume that teachers and students will enjoy and appreciate."&#151;Thomas Banchoff, Brown University<P>"Bill Dunham has done it again. <i>The Calculus Gallery</i> is a masterly journey through the works of thirteen mathematicians who formulated, formalised, and reformed the calculus into the modern analysis we learn today. Readers of his earlier books have learned to expect a clarity of exposition that few others can attain&#58; they will not be disappointed."&#151;Robin Wilson, author of <i>Four Colors Suffice</i><P>"This is an excellent book&#151;an amazing mathematical page-turner. William Dunham has done the seemingly impossible&#58; he has taken some difficult, advanced mathematics and, without sacrificing the technical details, written a lively, readable book about it."&#151;Barry Cipra, author of <i>Misteaks . . . and How to Find Them Before the Teacher Does</i><P>"Pedagogically excellent and extremely well written, <i>The Calculus Gallery</i> bridges the gap between general histories and detailed studies of individual mathematicians. Dunham has described mathematical developments in an engaging style rarely found in literature of this kind."&#151;Annette Imhausen, Trinity Hall, Cambridge<P>"A welcome addition to the literature. The idea of presenting a 'museum of mathematics' is new. It allows the author to present a nonstandard selection of theorems, so that even mathematicians with a strong historical background will learn a few things."&#151;Franz Lemmermeyer, Bilkent University, author of <i>Reciprocity Laws&#58; From Euler to Eisenstein</i></p> <h3>Eberhard Knobloch - Zentralblatt MATH Database</h3> <p>A fascinating, competent visit too the calculus gallery.</p>

"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. William Dunham 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."--Jacket

Ben shu jie shao liao shi duo wei you xiu de shu xue jia : niu dun, lai bu ni ci, bo nu li xiong di, ou la, ke xi, li man, liu wei er, wei er si te la si, kang tuo er, wo er tai la, bei er, le bei ge . ran er, zhe bu shi yi ben shu xue jia de chuan ji, er shi yi zuo zhan shi wei ji fen hong wei hua juan de chen lie shi . zuo zhe xuan ze jie shao liao li shi shang de ruo gan jie zuo (zhong yao ding li), you ya di cheng xian liao wei ji fen cong chuang jian dao wan shan de man chang, qu zhe de guo cheng

本书介绍了十多位优秀的数学家:牛顿, 莱布尼茨, 伯努利兄弟, 欧拉, 柯西, 黎曼, 刘维尔, 魏尔斯特拉斯, 康托尔, 沃尔泰拉, 贝尔, 勒贝格.然而, 这不是一本数学家的传记, 而是一座展示微积分宏伟画卷的陈列室.作者选择介绍了历史上的若干杰作(重要定理), 优雅地呈现了微积分从创建到完善的漫长, 曲折的过程

Isaac Newton (1642-1727) stands as a seminal figure not just in mathematics but in all of Western intellectual history.

Betr. die Brüder Jakob und Johann Bernoulli sowie Leonhard Euler (S. 35-68)

2021-09-08