The Early Mathematics of Leonhard Euler莱昂哈德·欧拉的早期数学
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作者： C. Edward Sandifer 著
出 版 社：
出版时间： 2007-2-1字数：版次： 1页数： 391印刷时间： 2007/02/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780883855591包装： 精装内容简介
The Early Mathematics of Leonhard Euler gives an article-by-article description of Leonhard Euler s early mathematical works, the 50 or so mathematical articles he wrote before he left St. Petersburg in 1741 to join the Academy of Frederick the Great in Berlin. These early pieces contain some of Euler s greatest work, the Königsberg bridge problem, his solution to the Basel problem, and his first proof of the Euler-Fermat theorem. It also presents important results that we seldom realize are due to Euler; that mixed partial derivatives are (usually) equal, our f(x) notation, and the integrating factor in differential equations. The books shows how contributions in diverse fields are related, how number theory relates to series, which, in turn, relate to elliptic integrals and then to differential equations. There are dozens of such strands in this beautiful web of mathematics. At the same time, we see Euler grow in power and sophistication, from a young student when at 18 he published his first work on differential equations (a paper with a serious flaw) to the most celebrated mathematician and scientist of his time. It is a portrait of the world s most exciting mathematics between 1725 and 1741, rich in technical detail, woven with connections within Euler s work and with the work of other mathematicians in other times and places, laced with historical context.
Describing Euler’s early mathematical works, this book is a portrait of the world’s most exciting mathematics between 1725 and 1741, rich in technical detail. Woven with connections within Euler’s work and with the work of other mathematicians in other times and places, laced with historical context.
作者简介
C. Edward Sandifer received his AB from Dartmouth College 1973, and his MA, PhD, from the University of Massachusetts, Amherst 1975, 1980. He was Chair of the Northeastern Section of the MAA, 1998-2000, and Secretary of The Euler Society, 2002-present. He is also a member of the American Mathematical Society, the Canadian Society for the History and Philosophy of Mathematics, and the British Society for the History of Mathematics. He is one of the founding members of The Euler Society, and on the charter committee at the founding of the History of Mathematics Special Interest Group of the MAA (HoMSIGMAA). He has run 34 consecutive Boston Marathons and won the 1984 Northeastern (USA) Regional Marathon Championship.
目录
Preface
Interlude: 1725-1727
1. Construction of isochronal curves in any kind of resistant
2. Method of finding reciprocal algebraic trajectories
Interlude: 1728
3. Solution to problems of reciprocal trajectories
4. A new method of reducing innumerable differential equations of the second degree to equations of the first degreeIntegrating factor
Interlude: 1729-1731
5. On transcendental progressions, or those for which the general term cannot be given algebraically
6. On the shortest curve on a surface that joins any two given points
7. On the summation of innumerably many progressions
Interlude: 1732
8. General methods for summing progressions
9. Observations on theorems that Fermat and others have looked at about prime numbers
10. An account of the solution of isoperimetric problems in the broadest sense
Interlude: 1733
11. Construction of differential equations which do not admit separation of variables
12. Example of the solution of a differential equation without separation of variables
13. On the solution of problems of Diophantus about integer numbers;
14. Inferences on the forms of roots of equations and of their orders
15. Solution of the differential equation axn dx = dy + y2dx
Interlude: 1734
16. On curves of fastest descent in a resistant medium
17. Observations on harmonic progressions
……
Interlude: 1735
Interlude: 1736
Interlude: 1737
Interlude: 1738
Interlude: 1739
Interlude: 1740
Interlude: 1741
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Index
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