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The Age of Euler

The Age of Euler. Nicholaus 1623-1708. Nicholaus I 1662-1716. Jakob I 1654-1705. Johann I 1667-1748. Nicholaus II 1662-1716. Nicholaus III 1695-1726. Johann II 1710-1795. Daniel I 1700-1782. Jakob II 1759-1789. Daniel II 1751-1834. Christoph 1751-1834. Johann Gustave 1751-1834.

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The Age of Euler

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  1. The Age of Euler

  2. Nicholaus 1623-1708 Nicholaus I 1662-1716 Jakob I 1654-1705 Johann I 1667-1748 Nicholaus II 1662-1716 Nicholaus III 1695-1726 Johann II 1710-1795 Daniel I 1700-1782 Jakob II 1759-1789 Daniel II 1751-1834 Christoph 1751-1834 Johann Gustave 1751-1834 Johann III 1746-1807 The Bernoullis Images from MacTutor

  3. Leonard Euler Images from MacTutor

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

  5. 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)

  6. 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 5th degree and above • Lagrange – Also attempts to find a general solution for the nth degree eq. • Number theory • Euler – Gives his proof of Fermat’s Last Theorem for n = 3.

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