Green's Functions : Construction and Applications

Cover......Page 1
Title......Page 4
Copyright......Page 5
Preface......Page 8
Contents......Page 12
0 Introduction......Page 14
1.1 Standard Procedure for Construction......Page 22
1.2 Symmetry of Green’s Functions......Page 38
1.3 Alternative Construction Procedure......Page 46
1.4 Chapter Exercises......Page 64
2.1 Method of Images......Page 68
2.2 Conformal Mapping......Page 87
2.3 Method of Eigenfunction Expansion......Page 93
2.4 Three-Dimensional Problems......Page 135
2.5 Chapter Exercises......Page 141
3.1 Definition of Green’s Function......Page 143
3.2 Method of Images......Page 146
3.3 Method of Eigenfunction Expansion......Page 158
3.4 Three-Dimensional Problems......Page 173
3.5 Chapter Exercises......Page 178
4. Higher Order Equations......Page 180
4.1 Definition of Green’s Function......Page 181
4.2 Rectangular-Shaped Regions......Page 182
4.3 Circular-Shaped Regions......Page 193
4.4 The equation ∇2∇2w(P) + λ4w(P) = 0......Page 212
4.5 Elliptic Systems......Page 219
4.6 Chapter Exercises......Page 236
5. Multi-Point-Posed Problems......Page 239
5.1 Matrix of Green’s Type......Page 240
5.2 Influence Function of a Multi-Span Beam......Page 251
5.3 Further Extension of the Formalism......Page 263
5.4 Chapter Exercises......Page 276
6.1 Introductory Comments......Page 278
6.2 Construction of Matrices of Green’s Type......Page 281
6.3 Fields of Potential on Surfaces of Revolution......Page 306
6.4 Chapter Exercises......Page 328
7. Diffusion Equation......Page 330
7.1 Basics of the Laplace Transform......Page 331
7.2 Green’s Functions......Page 335
7.3 Matrices of Green’s Type......Page 363
7.4 Chapter Exercises......Page 373
8. Black-Scholes Equation......Page 375
8.1 The Fundamental Solution......Page 376
8.2 Other Green’s Functions......Page 383
8.3 A Methodologically Valuable Example......Page 401
8.4 Numerical Implementations......Page 406
8.5 Chapter Exercises......Page 414
Appendix Answers to Chapter Exercises......Page 415
Bibliography......Page 434
Index......Page 440