Calculus of variations变分法

书籍目录

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

作者简介

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．

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