دانلود کتاب Green's Functions: Construction and Applications

فهرست مطالب :

Preface\n0 Introduction\n1 Green’s Functions for ODE\n 1.1 Standard Procedure for Construction\n 1.2 Symmetry of Green’s Functions\n 1.3 Alternative Construction Procedure\n 1.4 Chapter Exercises\n2 The Laplace Equation\n 2.1 Method of Images\n 2.2 Conformal Mapping\n 2.3 Method of Eigenfunction Expansion\n 2.4 Three-Dimensional Problems\n 2.5 Chapter Exercises\n3. The Static Klein-Gordon Equation\n 3.1 Definition of Green’s Function\n 3.2 Method of Images\n 3.3 Method of Eigenfunction Expansion\n 3.4 Three-Dimensional Problems\n 3.5 Chapter Exercises\n4 Higher Order Equations\n 4.1 Definition of Green’s Function\n 4.2 Rectangular-Shaped Regions\n 4.3 Circular-Shaped Regions\n 4.4 The equation ∇2∇2w(P) + λ4w(P) = 0\n 4.5 Elliptic Systems\n 4.6 Chapter Exercises\n5 Multi-Point-Posed Problems\n 5.1 Matrix of Green’s Type\n 5.2 Influence Function of a Multi-Span Beam\n 5.3 Further Extension of the Formalism\n 5.4 Chapter Exercises\n6 PDE Matrices of Green’s type\n 6.1 Introductory Comments\n 6.2 Construction of Matrices of Green’s Type\n 6.3 Fields of Potential on Surfaces of Revolution\n 6.4 Chapter Exercises\n7 Diffusion Equation\n 7.1 Basics of the Laplace Transform\n 7.2 Green’s Functions\n 7.3 Matrices of Green’s Type\n 7.4 Chapter Exercises\n8 Black-Scholes Equation\n 8.1 The Fundamental Solution\n 8.2 Other Green’s Functions\n 8.3 A Methodologically Valuable Example\n 8.4 Numerical Implementations\n 8.5 Chapter Exercises\nAppendix Answers to Chapter Exercises\nBibliography\nIndex