The Age of Euler. The Bernoullis Images from MacTutor Jakob I 1654-1705 Johann I 1667-1748 Nicholaus III 1695-1726 Daniel I 1700-1782 Johann II 1710-1795.

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Presentation transcript:

The Age of Euler

The Bernoullis Images from MacTutor Jakob I Johann I Nicholaus III Daniel I Johann II Nicholaus I Nicholaus II Nicholaus Jakob II Johann III Daniel II Christoph Johann Gustave

Leonard Euler Images from MacTutor

Joseph Louis Lagrange Guillaume François l’Hôpital Maria Gaetana Agnesi Jean Le Rond d’Alembert Bishop George Berkeley Colin Maclaurin Thomas Simpson

Calculus Texts in the 1700’s England (fluxions) Charles Hayes – A Treatise of Fluxions Simpson – A New Treatise of Fluxions (1737) Maclaurin – A Treatise of Fluxions (1742) Continental Europe (differentials) l’Hôpital – Analysis of Infinitely Small Quantities… (1690) Maria Agnesi – Foundations of Analysis for the Use of Italian Youth (1748) Euler – Introduction to Analysis of the Infinite (1748), Methods of Differential Calculus (1755), Methods of the Int. C. (1768) Lagrange – The Theory of Analytic Functions, containing the principles of the differential calculus, released…quantities (1797)

Algebra and Number Theory Systems of linear equations Maclaurin – Introduces Cramer’s Rule (before Cramer!) (1730’s) Polynomial equations Maclaurin – Gives well-organized form for solving polynomial equations through degree 4 and Newton’s numerical approx. method Euler – Gives a fuller treatment and notes that he cannot give any formulas for 5 th degree and above Lagrange – Also attempts to find a general solution for the n th degree eq. Number theory Euler – Gives his proof of Fermat’s Last Theorem for n = 3.