Calculus of variations變分法

內容介紹

This book by Robert Weinstock was written tO fill the need for a basic introduction to the calculus of variations．Simply and easilv written．with an emphasis 011 the applications of this calculus．it has long beell a standard refm ence of physicists，engineers and applied mathmn aticians
The author begins slowly，introducing the readel"to the calculus of variations，and supplying lists of essential formulae and derivations．Later chapters cover isoperimetric problem s，geometrical optics，Fennat’s principle．dynamiCS of particles．the SfLUm—Liouville eigenvalue·eigenfunction problem，the theory of elasticity，quan-tunl mechanics，and electrostatics．Each chapter ends with a series of exercises which shoukl prove veiv useful in deterlniningⅥrhether the material in that chapter has been thorotlghly grasped．
The clarity of exposition makes this book easily accessible tO anV。one who has mastered irst—year calculus with SOIlle exposure to ordinary differential equations Physicists and engineers who find variational methods evasive at times will find this book particularly helpful．

作品目錄

PREFACE
CHAPTER 1 INTRODUCTION
CHAPTER 2 BACKGROUND PRELIMINARIES
CHAPTER 3 INTRODUCTORY PROBLEMS
CHAPTER 4 ISOPERIMETRIC PROBLEMS
CHAPTER 5 GEOMETRICAL OPTICS: FERMAT'S PRINCIPLE
CHAPTER 6 DYNAMICS OF PARTICLES
CHAPTER 7 TWO INDEPENDENT VARIABLES: THE VIBRATING STRING
CHAPTER 8 THE STURM-LIOUVILIE OIGENVALUE-EIGENFUNG-TION PROBLEM
CHAPTER 9 SEVERAL INDEPENDENT VARIABLES: THE VIBRAT-ING MEMBRANE
CHAPTER 10 THEORY OF ELASTICITY
CHAPTER 11 QUANTUM MECHANICS
CHAPTER 12 ELECTROSTATICS
BIBLIOGRAPHY
INDEX