The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and 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 subject's 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.
In this new edition, several new exercises have been added. The book, containing a total of 119 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Sample Chapter(s)
Introduction (135 KB)
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Contents:
- Introduction
- Preliminaries
- Classical Methods
- Direct Methods: Existence
- Direct Methods: Regularity
- Minimal Surfaces
- Isoperimetric Inequality
- Solutions to the Exercises
- Bibliography
- Index
Readership: Graduate and undergraduate students taking a course in analysis and differential equations.
“A lot of new material has been added, in particular, complements and exercises. The book is recommended not only for students but also for scientists from other disciplines that want approach the fascinating field of variational problems.”
Mathematical Reviews Clippings
Reviews of the First Edition:
“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 detail put in. He obviously cares about actually teaching and not just covering material.”
SIAM Review
“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) exercise 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 of 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.”
Mathematical Association of America online book review
“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.”
Professor Ji-Huan He
Donghua University, Shanghai
