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Green's Functions : Construction and Applications.
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
De Gruyter,
2012.
|
| Colección: | De Gruyter studies in mathematics ;
42. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Melnikov, Yu. A. | |
| 245 | 1 | 0 | |a Green's Functions : |b Construction and Applications. |
| 260 | |a Berlin : |b De Gruyter, |c 2012. | ||
| 300 | |a 1 online resource (448 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematics, |x 0179-0986 ; |v 42 | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a 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. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references and index. | ||
| 546 | |a In English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Green's functions. | |
| 650 | 4 | |a Elliptisch. | |
| 650 | 4 | |a Greensche Funktion. | |
| 650 | 4 | |a Parabolisch. | |
| 650 | 4 | |a Partielle Differenzialgleichung. | |
| 650 | 6 | |a Fonctions de Green. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x Partial. |2 bisacsh | |
| 650 | 7 | |a Green's functions. |2 fast |0 (OCoLC)fst00947660 | |
| 650 | 7 | |a Green-Funktion |2 gnd | |
| 653 | |a Elliptic. | ||
| 653 | |a Green's Function. | ||
| 653 | |a Parabolic. | ||
| 653 | |a Partial Differential Equation. | ||
| 700 | 1 | |a Melnikov, Max Y. | |
| 776 | 0 | 8 | |i Print version: |a Melnikov, Yuri A. |t Green's Functions : Construction and Applications. |d Berlin : De Gruyter, ©2012 |z 9783110253023 |
| 830 | 0 | |a De Gruyter studies in mathematics ; |v 42. |x 0179-0986 | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=448094 |z Texto completo |
| 880 | 0 | |6 505-00/(S |a 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 Function -- 4.2 Rectangular-Shaped Regions -- 4.3 Circular-Shaped Regions -- 4.4 The equation ∇2∇2w(P) + λ4w(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 Functions -- 7.3 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. | |
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