The Early Mathematics of Leonhard Euler

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MAA, Mar 15, 2007 - Mathematics - 391 pages
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Describes Euler's early mathematical works - the 50 mathematical articles he wrote before he left St. Petersburg in 1741 to join the Academy of Frederick the Great in Berlin. These works contain some of Euler's greatest mathematics: the Konigsburg bridge problem, his solution to the Basel problem, his first proof of the Euler-Fermat theorem. Also presented are important results that we seldom realize are due to Euler: that mixed partial derivatives are equal, our f(x) notation, and the integrating factor in differential equations. The 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.
 

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Contents

17251727 I
1
1728
13
Nova methodus innumerabiles aequationes differentialis secundi
22
17291731
31
1732
65
Observationes de theoremate quodam Fermatiano aliisque
74
1733
89
De solutione problematum Diophanteorum per numeros integros
102
Curvarum maximi minimive proprietate gaudentium inventio
212
1737
227
Variae observationes circa series infinitas
249
1738
269
De aequationibus differentialibus quae certis tantum casibus
279
1739
299
De fractionibus continuis observationes
306
Consideratio progressionis cuiusdam ad circuli quadraturam
317

Constructio aequationis differentialis ax dx dy+y2dx
114
1734
123
De progressionibus harmonicis observationes
133
Additamentum ad dissertationem de infinitis curvis
148
1735
155
Methodus universalis serierum convergentium summas quam
166
De constructione aequationum ope motus tractorii aliisque
176
Solutio problematum rectificationem ellipsis requirentium
188
Solutio problematis ad geometriam situs pertinentis
195
1736
201
Methodus facilis computandi angulorum sinus ac tangentes
323
De seriebus quibusdam considerationes
342
1740
349
De extractione radicum ex quantitatibus irrationalibus
357
1741
365
Observationes analyticae variae de combinationibus
371
Commentatio de matheseos sublimioris utilitate
381
Topically Related Articles
386
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References to this book

Euler as Physicist
Dieter Suisky
Limited preview - 2008

About the author (2007)

Ed Sandifer is Professor of Mathematics of Western Connecticut State University. He earned his PhD at the University of Massachusetts under John Fogarty, studying ring theory. He became interested in Euler while attending the Institute for the History of Mathematics and Its Uses in Teaching, IHMT, several summers in Washington DC, under the tutelage of Fred Rickey, Victor Katz and Ron Calinger. Because of a series of advising mistakes, as an undergraduate he studied more foreign languages than he had to, so now he can read the works of Euler in their original Latin, French and German. Occasionally he reads Spanish colonial mathematics in its original as well. Now he is secretary of the Euler Society, and he writes a monthly on-line column, How Euler Did It, for the MAA. He and hi wife Theresa, live in a small town in western Connecticut, and he has run the Boston Marathon every year since 1973.