Calulus of Variations

Authors: Freguglia, Paolo, Giaquinta, Mariano
Thoroughly examines key early developments in the calculus of variations, from the brachystochrone problem to Lagrange’s δ-calculus
Guides the reader through the original works of Euler, Lagrange, the Bernoullis, and others that built up the theory, with instructive commentaries and supplemental information
Offers a unique perspective as a collaboration between a historian of mathematics and a mathematician
Provides insight for those studying the calculus of variations by naturally motivating its fundamental tools and concepts

The calculus of variations has a long history of interaction with other branches of mathematics such as geometry and differential equations, and with physics, particularly mechanics. More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations.