Calculus of Variations Charles Maccluer

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.

The book contains a wealth of material essential to the researcher concerned with multiple integral variational problems and with elliptic partial differential equations. The book not only reports the researches of the author but also the contributions of his contemporaries in the same and related fields.

This publication is a Special Issue of the journal Axioms entitled “Calculus of Variations, Optimal Control and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th birthday”. This Special Issue is dedicated to Professor Delfim F. M. Torres on his 50th birthday, as a recognition of his significant contributions to Mathematics, in particular regarding the calculus of variations, optimal control, and mathematical biology. Professor Torres is a distinguished University Professor, a highly cited researcher in Mathematics (in the top 1% for Mathematics in the Web of Science in 2015, 2016, 2017, and 2019), and a lifetime member of the American Mathematical Society.