Bernoulli family and the solution of the Bernoulli differential equation

Document Type : Research Paper

Authors

Yazd University

Abstract

The Bernoulli differential equation is a fascinating topic with significant applications in mathematics, engineering, and physics. In this article, we explore the history of the emergence and expansion of the Bernoulli differential equation. We also delve into the role of scholars who have attempted to solve this equation, notably the Bernoulli family, which, over three generations, contributed eight mathematicians to the community. Jacob, Daniel, and Johann Bernoulli played a prominent role in solving this equation. Finally, we examine the applications of the Bernoulli differential equation.

Keywords

Main Subjects


[1] http://www.thefamouspeople.com
[2] G. Piella, Adaptive wavelets and their applications to image fusion and compression, Ph. D. dissertation, Centre for Mathematics and Computer Science, University of Amsterdam, 2003.
[3] M. Kline, Mathematical Thought From Ancient to Modern Times, 2, Oxford University Press, New York, 1990.
[4] Ja. Bernoulli and Jo. Bernoulli, Die Streitschriften von Jacob und Johann Bernoulli, Variationsrechnung, H. Goldstine, ed., Birkh¨auser Verlag Press, Basel, 1991.
[5] Jo. Bernoulli, De conoidibus et spaeroidibus quaedam. Solutio analytica æquationis in Actis A, 1695, pp. 553 propositæ (A Fratre Jac. Bernoullio), Acta Eruditorum, (1697) 113–118.
[6] E. L. Ince, Ordinary Differential Equations, Dover Press, New York, 1944.
[7] I. Newton, The Mathematical Papers of Isaac Newton, 3, D. T. Whiteside, ed., Cambridge University Press, Cambridge, 1981.
[8] E. Hairer and G. Wanner, Analysis By Its History, Undergraduate Texts in Mathematics, Springer Verlag, New York, 2008.
[9] G. W. Leibniz, Notatiuncla ad Acta Decemb, 1695, pp. 537 et seqq., Acta Eruditorum, (1696) 145-147.
[10] A. E. Parker, Who Solved the Bernoulli Differential Equation and How Did They Do It?, 44, 2013 the college mathematics journal.
[11] John E. Sasser, History of ordinary differential equations The first hundred years, Mathematics and Applied Sciences University of Cincinnati.
[12] http://scitech.blogsky.com/1390/11/25/post-309/.
[13] Mathematische Schriften, Band III/1, Briefwechsel Zwischen Leibniz, Jacob Bernoulli, Johann Bernoulli und Nicolaus Bernoulli, C. I. Gerhardt, ed., Halle, 1855.