TY  - BOOK
AU  - Melnikov,YuA.
AU  - Melnikov,Max Y.
TI  - Green's Functions: Construction and Applications
T2  - De Gruyter studies in mathematics,
SN  - 9783110253399
AV  - QC174.17.G68 M45 2011 
U1  - 515.353515/.353 
PY  - 2012///
CY  - Berlin
PB  - De Gruyter
KW  - Green's functions
KW  - Elliptisch
KW  - Greensche Funktion
KW  - Parabolisch
KW  - Partielle Differenzialgleichung
KW  - Fonctions de Green
KW  - MATHEMATICS
KW  - Differential Equations
KW  - Partial
KW  - bisacsh
KW  - fast
KW  - Green-Funktion
KW  - gnd
KW  - Elliptic
KW  - Green's Function
KW  - Parabolic
KW  - Partial Differential Equation
KW  - Electronic books
N1  - Includes bibliographical references and index; Preface; 0 Introduction; 1 Green's Functions for ODE; 1.1 Standard Procedure for Construction; 1.2 Symmetry of Green's Functions; 1.3 Alternative Construction Procedure; 1.4 Chapter Exercises; 2 The Laplace Equation; 2.1 Method of Images; 2.2 Conformal Mapping; 2.3 Method of Eigenfunction Expansion; 2.4 Three-Dimensional Problems; 2.5 Chapter Exercises; 3. The Static Klein-Gordon Equation; 3.1 Definition of Green's Function; 3.2 Method of Images; 3.3 Method of Eigenfunction Expansion; 3.4 Three-Dimensional Problems; 3.5 Chapter Exercises; 4 Higher Order Equations; 4.1 Definition of Green's Function4.2 Rectangular-Shaped Regions; 4.3 Circular-Shaped Regions; 4.4 The equation?2?2w(P) +?4w(P) = 0; 4.5 Elliptic Systems; 4.6 Chapter Exercises; 5 Multi-Point-Posed Problems; 5.1 Matrix of Green's Type; 5.2 Influence Function of a Multi-Span Beam; 5.3 Further Extension of the Formalism; 5.4 Chapter Exercises; 6 PDE Matrices of Green's type; 6.1 Introductory Comments; 6.2 Construction of Matrices of Green's Type; 6.3 Fields of Potential on Surfaces of Revolution; 6.4 Chapter Exercises; 7 Diffusion Equation; 7.1 Basics of the Laplace Transform; 7.2 Green's Functions7.3 Matrices of Green's Type; 7.4 Chapter Exercises; 8 Black-Scholes Equation; 8.1 The Fundamental Solution; 8.2 Other Green's Functions; 8.3 A Methodologically Valuable Example; 8.4 Numerical Implementations; 8.5 Chapter Exercises; Appendix Answers to Chapter Exercises; Bibliography; Index
N2  - This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. This book is a useful source for everyone who is studying or working in the fields of science, finance, or engineering that involve practical solution of partial differential equations
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ER  -