The calculus of variations is one of the oldest subjects in mathematics, yet is very much alive and is still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology.

This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist — mathematicians, physicists, engineers, students or researchers — in discovering the subjects most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions.

The book, containing more than seventy exercises with detailed solutions, is well designed for a course both at the undergraduate and graduate levels.

Contents:

• Preliminaries
• Classical Methods
• Direct Methods
• Regularity
• Minimal Surfaces
• Isoperimetric Inequality
• Solutions to the Exercises

“This book provides non-mathematics students with an easy way to grasp the basic idea of the calculus of variations, and its possible applications in their field of study. For mathematics students, the book leads them to the very directions which should be followed.”

“This wonderful book is imbued with a marvelous historical perspective so that the reader is taught some very beautiful mathematics fitted in the proper historical perspective ... it is full of terrific hard analysis focused on a general theme that is exemplified by the author's astute and elegant choice of topics ... There are a lot of (outstanding) exercises and these are critical for a deeper understanding of the material. All of Chapter 7 is devoted to their solutions, and this increases the book's already considerable value as a source for self-study ... it's a very beautiful treatment, and will reward the diligent reader with a solid introduction to a great and grand subject and to a lot of beautiful hard analysis.”

"A great feature is the concluding Chapter 7, presenting complete solutions to all the exercises set earlier in the book ... This is a well thought-out selection, and Dacorogna's expert discussion is everywhere really clear and nicely motivated, with lots of details put in. He obviously cares about actually teaching and not just covering material."