The Early Mathematics of Leonhard Euler

C. Edward Sandifer

  • 出版商: The Mathematical Ass
  • 出版日期: 2007-03-15
  • 售價: $1,150
  • 貴賓價: 9.8$1,127
  • 語言: 英文
  • 頁數: 380
  • ISBN: 0883855593
  • ISBN-13: 9780883855591
  • 下單後立即進貨 (約5~7天)




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


《Leonhard Euler的早期數學》詳細描述了Leonhard Euler在1741年離開聖彼得堡前所寫的大約50篇數學文章,並在柏林的Frederick the Great學院加入之前。這些早期作品包含了Euler最偉大的工作,如Königsberg橋問題、他對Basel問題的解答以及他對Euler-Fermat定理的首次證明。書中還介紹了一些重要的結果,我們往往不自覺地歸功於Euler,例如混合偏導數(通常)相等、我們的f(x)表示法以及微分方程中的積分因子。這本書展示了不同領域的貢獻之間的關聯,數論與級數的關係,進而與橢圓積分和微分方程相關。在這個美麗的數學網絡中,有數十條這樣的線索。同時,我們可以看到Euler在力量和技巧上的成長,從一個年輕的學生,在18歲時發表了他的第一篇關於微分方程的論文(有一個嚴重的缺陷),成為當時最著名的數學家和科學家。這是一幅描繪了1725年至1741年間世界上最令人興奮的數學的肖像,充滿了技術細節,與Euler的其他工作以及其他時代和地方的數學家的工作相互交織,融合了歷史背景。