n 1722 the Italian mathematician Jacopo Ric- cati (1676–1754) held a course of lectures on differential equations, which remained unpublished until 1761. They finally emerged, under the title Della separazione delle in- determinate nelle equazioni differenziali del primo grado e della riduzione delle equazioni differenziali del secondo e di altri gradi ulteriori, in the first of four tomes of his Opera Omnia. This treatise, following the Leibniz (1646–1716) tradition of seeking solutions finitely expressed in terms of known functions, focuses on the separation of variables, to integrate a broad class of ordinary differential equations, of first or higher order. Its first part, entitled Dei metodi inventati da varj celebri Autori per separare le indeterminate nelle equazioni differenziali del primo grado, makes a survey of all relevant integrating methods, known at that time. These are thanks to Gabriele Manfredi (1681–1761), Jakob Bernoulli (1654–1705), his younger brother Johann (1667– 1748), Vincenzo Riccati (1707–1775), son of Jacopo, and Jacopo himself: our paper considers those of them, which in our opinion are the smartest and most ingenious.

Mingari Scarpello, G., Ritelli, D. (2019). FIRST ORDER DIFFERENTIAL EQUATIONS: EARLY HISTORY FOLLOWING JACOPO RICCATI AND GABRIELE MANFREDI. Mantova : Universitas Studiorum.

FIRST ORDER DIFFERENTIAL EQUATIONS: EARLY HISTORY FOLLOWING JACOPO RICCATI AND GABRIELE MANFREDI

Mingari Scarpello, Giovanni;Ritelli, Daniele
2019

Abstract

n 1722 the Italian mathematician Jacopo Ric- cati (1676–1754) held a course of lectures on differential equations, which remained unpublished until 1761. They finally emerged, under the title Della separazione delle in- determinate nelle equazioni differenziali del primo grado e della riduzione delle equazioni differenziali del secondo e di altri gradi ulteriori, in the first of four tomes of his Opera Omnia. This treatise, following the Leibniz (1646–1716) tradition of seeking solutions finitely expressed in terms of known functions, focuses on the separation of variables, to integrate a broad class of ordinary differential equations, of first or higher order. Its first part, entitled Dei metodi inventati da varj celebri Autori per separare le indeterminate nelle equazioni differenziali del primo grado, makes a survey of all relevant integrating methods, known at that time. These are thanks to Gabriele Manfredi (1681–1761), Jakob Bernoulli (1654–1705), his younger brother Johann (1667– 1748), Vincenzo Riccati (1707–1775), son of Jacopo, and Jacopo himself: our paper considers those of them, which in our opinion are the smartest and most ingenious.
2019
Molecular and mathematical biology, chemistry, medicine and medical statistics, bioinformatics and numerical analysis
205
236
Mingari Scarpello, G., Ritelli, D. (2019). FIRST ORDER DIFFERENTIAL EQUATIONS: EARLY HISTORY FOLLOWING JACOPO RICCATI AND GABRIELE MANFREDI. Mantova : Universitas Studiorum.
Mingari Scarpello, Giovanni; Ritelli, Daniele
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/752730
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact