The Early Mathematics of Leonhard Euler, Volumen 1MAA, 15 mar 2007 - 391 páginas "The Early Mathematics of Leonhard Euler 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. It also presents 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 provides some of the way mathematics is actually done. For example, Euler found partial results towards the Euler-Fermat theorem well before he discovered a proof of the Fermat theorem itself, and the Euler-Fermat version came 30 years later, beyond the scope of this book. The book shows how results 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 his first work on differential equations as an 18-year old student, a paper with a serious flaw in it, to the most celebrated mathematician and scientist of his times, when, at the age of 34, he was lured away like a superstar athlete might be traded today. 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."--Publisher's website. |
Índice
17251727 | 1 |
17291731 | 31 |
1732 | 65 |
Problematis isoperimetrici in latissimo sensu accepti | 79 |
1733 | 89 |
1734 | 123 |
1735 | 155 |
Inventio summae cuiusque seriei ex dato termino generali | 170 |
1736 | 201 |
1737 | 227 |
1738 | 269 |
1739 | 299 |
Consideratio progressionis cuiusdam ad circuli quadraturam | 317 |
Methodus facilis computandi angulorum sinus ac tangentes | 323 |
De seriebus quibusdam considerationes | 342 |
1740 | 349 |
De constructione aequationum ope motus tractorii aliisque | 176 |
Solutio problematum rectificationem ellipsis requirentium | 188 |
Solutio problematis ad geometriam situs pertinentis | 195 |
1741 | 365 |
Topically Related Articles 387 | |
Otras ediciones - Ver todo
The Early Mathematics of Leonhard Euler, Volumen 1 C. Edward Sandifer No hay ninguna vista previa disponible - 2007 |
The Early Mathematics of Leonhard Euler, Volumen 1 C. Edward Sandifer No hay ninguna vista previa disponible - 2007 |
Términos y frases comunes
Acad algebraic analysis angle arc length axis Basel Problem Bernoulli calculations calculus of variations circle coefficients Commentarii constant of integration continued fractions convergence Corollary curve Daniel Bernoulli decimal places denominators denote differential equation divided dx² ellipse equal Euler begins Euler gives Euler notes Euler says Euler takes Euler tells Euler turns Euler-Fermat Theorem Euler-Mascheroni constant evolute example expression factors Fermat formula function geometric geometric series given Goldbach harmonic series infinite product Johann Bernoulli logarithm mathematics method multiplies notation number theory odd numbers Opera Omnia paper Petersburg Petropol polynomial prime numbers progression proof quantities radius of curvature reader reciprocal trajectories relatively prime Riccati equation roots sequence solution solve square substitutes tangent Theorem values variables writes wrote zero