Mathematical Analysis - General & Miscellaneous, Matrices & Determinants, Mathematical Equations - Integral, Mathematical Equations - Differential

Handbook of Green's Functions and Matrices

Name: Handbook of Green's Functions and Matrices
Author: V.D. Sheremet
ISBN: 9781853129339

by V.D. Sheremet

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Overview

The book presents two decades of the author's scientific work.The presented results have been reported, partially published in Russian, discussed and approved at the prestigious scientific centres of the former USSR. The book contains Green's matrices for 320 boundary value problems of Lame equations, expressed in terms of the respective Green's functions for 228 boundary value problems of Poisson's operator, constructed for 19 domains of the Cartesian, polar and cylindrical coordinate system. It also includes some examples and methods of construction and application of Green's functions and matrices used to define the fields of deformations and stresses as well as the fields of the stationary temperature and electrostatics. A CD-ROM which features worked examples and solutions is also included.

The book will be a useful reference for students and specialists who deal with solving of boundary value problems of mechanics of deformable rigid bodies and of thermo- and electrostatics.

Designed for graduate and postgraduate students investigating such areas as elasticity, thermoelasticity, mechanics, heat conduction, elector and magneto conduction, electronics, radio-physics, hydrodynamics, and conduction of moisture, the text will also be of interest to engineers and researchers working in these fields.

Synopsis

In this book the author describes his own technique of constructing Green's functions and matrices for the elastostatic Lame's equations and provides examples of applications in applied mathematical physics.
Designed for graduate and postgraduate students investigating such areas as elasticity, thermoelasticity, mechanics, heat conduction, electro- and magneto conduction, electronics, radio-physics, hydrodynamics, and conduction of moisture, the text will also be of interest to engineers and researchers working in these fields.
Many problems and solutions are included while an accompanying CD-ROM features examples and applications of Green's functions for Poisson's equation, and 2D and 3D Green's matrices for Lame's equations.
Contents: Preface; Introduction; PART I - THE BASIS OF INCOMPRESSIBLE INFLUENCE ELEMENTS METHOD: Integral Representations of Solutions in the Theory of Elasticity; Constructive Solutions for Green's Matrices in the Form of Integrals. PART II - HANDBOOK OF GREEN'S FUNCTIONS AND MATRICES: Green's Functions and Matrices for Two-Dimensional Domains; Green's Functions and Matrices for Three-Dimensional Domains. Notations; References; Index.