Definition:Calculus of Variations/Historical Note
Historical Note on Calculus of Variations
Some sources suggest that, in a sense, the earliest problem in the calculus of variations arose in one of the legends of the founding of Carthage; the city was granted as much land as could be enclosed by a given length.
The calculus of variations emerged as a branch of mathematics as a result of investigations into the cycloid in the $18$th century.
The first systematic investigation of the topic was given by Joseph Louis Lagrange in his earliest and most important works, together with Leonhard Paul Euler, who coined the term in $1766$.
Karl Weierstrass ushered in a new era of precise reasoning with his lectures in $1879$ on the subject.
One of his students, Oskar Bolza, took on the subject and developed the Chicago school of the calculus of variations.
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{VIII}$: Nature or Nurture?
- 1963: Charles Fox: An Introduction to the Calculus of Variations (2nd ed.) ... (previous) ... (next): Chapter $\text I$. The First Variation: $1.1$. Introduction
- 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3$: Appendix $\text A$: Euler
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.15$: Torricelli ($\text {1608}$ – $\text {1647}$)
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.21$: Euler ($\text {1707}$ – $\text {1783}$)
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.22$: Lagrange ($\text {1736}$ – $\text {1813}$)
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($\text {1815}$ – $\text {1897}$)