Calculus of Variations & Solution Manual

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