Skip to main content
SpringerLink
Log in

…and so Euler discovered Differential Equations

  • Published:
Foundations of Science Aims and scope Submit manuscript

Abstract

Euler's contributions to differential equations are so comprehensive and rigorous that any contemporary textbook on the subject can be regarded as a copy of Euler's Institutionum Calculi Integralis. Of course, Euler's work is an improvement of that of Leibniz, the Bernoullis, Newton and so many others before them, but still it's so outstanding that will be used in this paper as a reference to account for every previous or subsequent development in ODEs. Maybe Euler did not discovered differential equations, but he did not discovered less differential equations than Newton and Leibniz had discovered differential calculus a few decades before.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bernoulli, J. (1690). Analysis problematis. de inventione lineae decensus a corpore gravi percurrenda uniformiter Acta Eruditorum, 217. http://www.izwtalt.uni-wuppertal.de.

  • Bernoulli, J. (1692/1991). ‘Meditationes CLXXXVII: Methodus reducendi in Aequationibus differentialibus differentias secundas ad primas’. In H. Goldstine (Ed) Die Streitschriften von Jakob und Johann Bernouilli: Variationsrechnung. Birkhäuser, Basel.

  • Bernoulli, J. (1694). Additamentum effectionis omnium quadraturarum et rectificationum curvarum per seriem quandam generalissimam. Acta Eruditorum, 13, 437–441.

    Google Scholar 

  • Bernoulli, J. (1695). Explicationes, annotationes et additiones ad ea quaein actis superiorum annorum de curva elastica, isochrona paracentrica, & velaria, hinc inde memorata, & partim controversa leguntur, ubi de linea mediarum directionum aliisque novis, Acta Eruditorum Dec 1695; available at http://www.izwtalt.uni-wuppertal.de/AE.html.

  • Bernoulli, J. (1696). Problema beaunianum universalius conceptum, sirve solution aequationis nupero Decembri propostae, ady = ypdx + by n qdx; cum aliis quibusdam annotates, Acta Eruditorum Jul (1696) 332; available at http://www.izwtalt.uni-wuppertal.de/AE.html.

  • Bernoulli, J. (1697). De conoidibus et spaeroidibus quaedam. Solutio analytica aequationis in Actis A. 1695.

  • Bernoulli, J. (1742). Opera omnia. In G. Cramer, vol. 4, Lausanne.

  • Bernoulli, D. (1924). Miscellanea Taurinensia, Ostwald'sKlassiker, Leipzig.

  • Bessel, F. (1824). Untersuchung des Theils der planetarishen Störungen, welcher aus der Bewegung der Sonne entsteht. Berliner Abh. 1824 (published 1826), pp. 1–52.

  • Bittanti, Sergio. (1991). The Riccati equation. Berlin: Springer.

    Book  Google Scholar 

  • Boyer, C. B. (1951). The foremost textbook of modern times. The American Mathematical Monthly, 58, 223–226.

    Article  Google Scholar 

  • Burton, D. M. (2005). The history of mathematics: An introduction (6th ed., p. 359). New York: McGraw-Hill. ISBN 978-0-07-305189-5.

    Google Scholar 

  • Chandrasekhar, S. (2005). Newton's Principia for the common reader. Oxford: Clarendon Press.

    Google Scholar 

  • Clairaut, A. (1739). Recherches générales sur le calcul integral (pp. 425–436). Turin: Mémoires de l’Academie Royale des Science.

    Google Scholar 

  • Clairaut, A. (1740). Sur l’intégration ou la construction des équations différetielles de premier ordre (pp. 293–323). Turin: Mémoires de l’Academie Royale des Science.

    Google Scholar 

  • Clairaut, A. (1752). Histoire de l’Academie royale des sciences et belles lettres, depuis son origine jusqu’a present. Aver les pieces originales. Paris 1734. Deutsche Akademie der Wissenschaften zu Berlin, Chez Haude et Spener, 1752.

  • Davis, P. J. (1959). Leonhard Euler’s integral: A historical profile of the gamma function. The American Mathematical Monthly, 66(10), 849–869.

    Google Scholar 

  • Euler, L. (1768). Institutionum Calculi Integralis. Petropoli, Impenfis Academiae Imperialis Scientiarum.

  • Goldstine, H. (1980). A history of the calculus of variations from the 17th through the 19th century. Berlin: Springer.

    Book  Google Scholar 

  • Hofmann, Joseph E. (1974). Leibniz in Paris, 1672-76: His growth to mathematical Maturity. Cambridge: Cambridge University Press.

    Google Scholar 

  • Ince, E. (1944). Ordinary differential equations. New York: Dover Press.

    Google Scholar 

  • Katz, V. (1998). A history of mathematics. An introduction: Addison-Wesley.

    Google Scholar 

  • Lagrange, J. L. (1774/1776). Sur les intégrales particuliers des équations différentielles, Nouv. Mém. Acad. Berlin 1774 (1776), pp. 197–275.

  • Lagrange, J. L. (1998). Recherche sur les suites récurrentes, Nouveaux Mém (pp. 183–272). Berlin: De l’Acad. Royale des Science et Belles-Lettres.

    Google Scholar 

  • Leibniz, G. (1684). Nova Methodus pro Maximis et Minimis. Acta Eruditorum 1684. http://www.izwtalt.uni-wuppertal.de/Acta.html.

  • Leibniz, G. (1689). Analysis problematis… de inventione lineae decensus a corpore gravi percurrenda uniformiter… De linea isochrona, in qua grave sine acceleratione descendit, et de controversia cum. Acta Eruditorum, 195, 1689. http://www.izwtalt.uni-wuppertal.de.

  • Leibniz, G. (1695). Notatiuncla ad Acta Decemb. 1695, p. 537 et seqq. Acta Eruditorum, Mar (1696 145–147; available at http://www.izwtalt.uni-wuppertal.de/AE.html.

  • Leibniz, G. (1849–1863). Mathematische Schriften. In C. J. Gerhardt, G. H. Pertz (Ed.) Gesammelte Werke. Third Series, Mathematik. vol. 7, Halle.

  • Leibniz, G. (1850). Mathematische Schriften, Band II, Briefwechsel Zwischen Leibniz, Hugens van Zulichem und dem Marquis de l'Hospital, C.I. Gerhardt, ed., D. Nutt, London.

  • Manfredi, G. (1707). On the Construction of First Degree Differential Equations (De constructione Aequationum Differentialium Primi Gradus).

  • May, K. O. (1975). Historiographic vices II priority chasing. Historia Mathematica, 2, 315–317. https://doi.org/10.1016/0315-0860(75)90072-5.

    Article  Google Scholar 

  • Parker, A. (2013). Who solved the bernoulli differential equation and how did they do it? The College Mathematics Journal, 44(2), 89–97.

    Article  Google Scholar 

  • Picard, Emile. (1890). Mémoire sur la théorie des équations aux différences partielles et la méthode d'approximations successives. Journal des mathématiques pures et appliquées IV, 6, 145–210.

    Google Scholar 

  • Riccati, J. (1723). Appendix ad animadversiones in aequationes differentiales secundi gradus. Acta Eruditorum, 1723; available at http://www.izwtalt.uni-wuppertal.de.

  • Sasser, J. (1992). History of ordinary differential equations: The first hundred years. http://www2.fiu.edu/~yuasun/ODE_History.pdf.

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de A Coruña, A Coruña, Spain

    Pablo Rodríguez-Vellando

Authors
  1. Pablo Rodríguez-Vellando
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pablo Rodríguez-Vellando.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rodríguez-Vellando, P. …and so Euler discovered Differential Equations. Found Sci 24, 343–374 (2019). https://doi.org/10.1007/s10699-018-9571-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10699-018-9571-1

Keywords

Search

Navigation