Calculus of Variations & Solution Manual

Russak

Table of contents :
Title……Page 1
Contents……Page 2
List of Figures……Page 3
Credits……Page 4
1.1 Unconstrained Minimum……Page 5
1.2 Constrained Minimization……Page 9
2 Examples, Notation……Page 14
2.1 Notation & Conventions……Page 17
2.2 Shortest Distances……Page 18
3 First Results……Page 25
3.1 Two Important Auxiliary Formulas:……Page 26
3.2 Two Important Auxiliary Formulas in the General Case……Page 30
Problems……Page 38
4 Variable End-Point Problems……Page 40
4.1 The General Problem……Page 42
4.2 Appendix……Page 45
Problems……Page 48
5 Higher Dimensional Problems……Page 50
5.1 Variational Problems with Constraints……Page 51
Problems……Page 61
6 Integrals Involving More Than One Independent Variable……Page 63
7.1 Indirect Methods……Page 67
7.2 Direct Methods……Page 78
8 The Rayleigh-Ritz Method……Page 86
8.1 Euler’s Method of Finite Differences……Page 88
9 Hamilton’s Principle……Page 94
10 Degrees of Freedom – Generalized Coordinates……Page 101
11 Integrals Involving Higher Derivatives……Page 108
12 Piecewise Smooth Arcs and Additional Results……Page 114
13 Field Theory Jacobi’s Neccesary Condition and Sufficiency……Page 120
Index……Page 132
— Solution Manual-01 —……Page 134
List of Figures……Page 136
1 Functions of n Variables……Page 138
2 Examples, Notation……Page 146
3 First Results……Page 150
4 Variable End-Point Problems……Page 170
5 Higher Dimensional Problems……Page 191
6 Integrals Involving More Than One Independent Variable……Page 211
7 Examples of Numerical Techniques……Page 217
8 The Rayleigh-Ritz Method……Page 222
9 Hamilton’s Principle……Page 228
10 Degrees of Freedom – Generalized Coordinates……Page 237
11 Integrals Involving Higher Derivatives……Page 239