Introduction to the Calculus of Variations (ePub)

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.Contents: IntroductionPreliminariesClassical MethodsDirect Methods: ExistenceDirect Methods: RegularityMinimal SurfacesIsoperimetric InequalitySolutions to the ExercisesBibliographyIndex Readership: Graduate and undergraduate students taking a course in analysis and differential equations.Key Features:Serves as an excellent introduction to the calculus of variationsUseful to researchers in different fields of mathematics who want to get a concise but broad introduction to the subjectIncludes more than 100 exercises with solutions