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.