E-Book, Englisch, Band Volume 19, 178 Seiten, Web PDF
Elsgolc / Sneddon / Stark Calculus of Variations
1. Auflage 2014
ISBN: 978-1-4831-3756-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band Volume 19, 178 Seiten, Web PDF
Reihe: International Series in Pure and Applied Mathematics
ISBN: 978-1-4831-3756-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter is illustrated by a large number of problems some of which are taken from existing textbooks. The solutions to the problems in each chapter are provided at the end of the book.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Calculus of Variations;4
3;Copyright Page;5
4;Table of Contents;6
5;FROM THE PREFACE TO THE FIRST RUSSIAN EDITION;8
6;INTRODUCTIOiN;10
7;CHAPTER I. THE METHOD OF VARIATION IN PROBLEMS WITH FIXED BOUNDARIES;14
7.1;1. The variation and its properties;14
7.2;2. Euler equation;24
7.3;3. Functionals of the form;40
7.4;4. Functionals involving derivatives of higher order;43
7.5;5. Functionals depending on functions of several independent variables;48
7.6;6. Parametric representation of variational problems;55
7.7;7. Some applications;59
7.8;Problems;63
8;CHAPTER II. VARIATIONAL PROBLEMS WITH MOVABLE BOUNDARIES AND SOME OTHER PROBLEMS;65
8.1;1. Simplest problem with movable boundaries;65
8.2;2. Problems with movable boundaries for functionals of the form;73
8.3;3. Problems with movable boundaries for functionals of the form;80
8.4;4. Extremals with cusps;84
8.5;5. One-sided variations;95
8.6;6. Mixed problems;99
8.7;Problems;101
9;CHAPTER III. SUFFICIENCY CONDITIONS FOR AN EXTREMUM;104
9.1;1. Fields of extremals;104
9.2;2. The function;112
9.3;Problems;127
10;CHAPTEK IV. VARIATIONAL PROBLEMS OF CONSTRAINED EXTREMA;128
10.1;1. Constraints of the form;128
10.2;2. Constraints of the form;137
10.3;3. Isoperimetric problems;140
10.4;Problems;147
11;CHAPTER V. DIRECT METHODS OF SOLVING VARIATIONAL PROBLEMS;149
11.1;1. Direct methods;149
11.2;2. Euler method of finite differences;151
11.3;3. Ritz's method;154
11.4;4. Kantorovic's method;166
11.5;Problems;172
12;SOLUTIONS TO THE PROBLEMS;174
13;INDEX;178
