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D'Alembert, Lagrange, and Reduction of Order - References

Sarah Cummings (Wittenberg University) and Adam E. Parker (Wittenberg University)

[1]  A. Alexander. Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics (dissertation). President and Fellows of Harvard College, Boston, 2010. Also available in revised version, Harvard Univ. Press, 2011.

[2]  W. E. Boyce and R. C. DiPrima. Elementary Differential Equations. Wiley, New York, 10th edition, 2012.

[3]  J. L. R. d'Alembert. Extract de différentes lettres de M. d'Alembert à M. De La Grange écrites pendant les années 1764 & 1765. Misc. Taurinensia, 3:381-396, 1766. Available online via Google Books.

[4]  S. S. Demidov. On the history of the theory of linear differential equations. Arch. Hist. Exact Sci., 28:369-387, 1983.

[5]  L. P. Euler. De integratione aequationum differentialium altiorum graduum. Misc. Berolinensia, 7:193-242, 1743. Available online at MAA Euler Archive as E62.

[6]  L. P. Euler. Observatio singularis circa aequationes differentiales lineares. Nova Acta Academiae Scientarum Imperialis Petropolitinae, 14:52-61, 1805. Available online at MAA Euler Archive as E720.

[7]  J. Fauvel and J. Gray. The History of Mathematics: A Reader. Macmillan Press, London, 1987.

[8]  Thomas L. Hankins. Jean d'Alembert: Science and the Enlightenment. Gordon and Breach Science, New York, 1970.

[9]  E. L. Ince. Ordinary Differential Equations. Dover Publications, New York, 1944.

[10]  M. Kline. Mathematical Thought From Ancient to Modern Times, volume 2. Oxford Univ. Press, 1972.

[11]  J. L. Lagrange. Solution de différens problêmes de calcul intégral. Misc. Taurinensia, 3:179-380, 1766. Available online via Google Books.

[12]  J. L. Lagrange. Oeuvres, volume 13. Gauthier-Villars, Paris, 1882. Our source was a copy held by Bibliothèque nationale de France (BNF), département Littérature et art, V-15599 (BIS), available online via Gallica.

[13]  J.J. O’Connor and E.F. Robertson, Jean Le Rond d'Alembert, MacTutor History of Mathematics Archive. October 1998.

[14]  D. E. Otero. History helps make sense. Math Horizons, pp. 10-20, April 2015.

[15]  D. Zill. A First Course in Differential Equations: The Classic Fifth Edition. Cengage, Pacific Grove CA, 2000.

[16]  D. Zwillinger. Handbook of Differential Equations. Academic Press, Waltham Mass., 3rd edition, 1997, reprinted 2007. Available online in pdf format.

Sarah Cummings (Wittenberg University) and Adam E. Parker (Wittenberg University), "D'Alembert, Lagrange, and Reduction of Order - References," Convergence (September 2015)