Green's Functions : Construction and Applications.

By:

Melnikov, Yu. A

Contributor(s):

Melnikov, Max Y

Material type: Text

TextSeries: De Gruyter studies in mathematics ; 42.Publication details: Berlin : De Gruyter, 2012.Description: 1 online resource (448 pages)Content type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783110253399
3110253399
311025302X
9783110253023
9781280597640
128059764X
9786613627476
661362747X

Subject(s): Genre/Form:

Additional physical formats: Print version:: Green's Functions : Construction and Applications.DDC classification:

515.353 515/.353

LOC classification:

QC174.17.G68 M45 2011

Other classification:

35-02 | 35J08 | 35J25 | 35J40 | 35K20 | 35R05 | 65N80 | 74Kxx | 34B27
SK 470

Online resources:

Click here to access online

Contents:

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.

Summary: 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.

Item type:

Tags from this library: No tags from this library for this title. Log in to add tags.

Average rating: 0.0 (0 votes)

Holdings
Item type	Home library	Collection	Call number	Materials specified	Status	Date due	Barcode
Electronic-Books	OPJGU Sonepat- Campus	E-Books EBSCO			Available

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.