Green s Functions Potential Fields on Surfaces 1st Edition by Yuri Melnikov 3319572437 9783319572437

Green s Functions Potential Fields on Surfaces 1st Edition by Yuri A. Melnikov – Ebook PDF Instant Download/DeliveryISBN:  3319572437, 9783319572437 

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ISBN-10 :  3319572437

ISBN-13 :  9783319572437

Author:  Yuri A. Melnikov  

This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green’s functions from scratch. Green’s functions is an instrument easily accessible to practitioners who are engaged in design and exploitation of machines and structures in modern engineering practice. To date, there are no books available on the market that are devoted to the Green’s function formalism for equations covered in this volume. The reader, with an undergraduate background in applied mathematics, can become an active user of the Green’s function approach. For the first time, Green’s functions are discussed for a specific class of problems dealing with potential fields induced in thin-wall structures and therefore, the reader will have first-hand access to a novel issue. This Work is accessible to researchers in applied mathematics, mechanics, and relevant disciplines such as engineering, as well as to upper level undergraduates and graduate students.

Green s Functions Potential Fields on Surfaces 1st table of contents:

1 Green’s Functions for ODE
1.1 Two-Point-Posed Boundary Value Problems
1.1.1 Existence and Uniqueness Theorem
1.1.2 Symmetry of Green’s Functions
1.1.3 An Alternative Procedure
1.2 Multiple-Point-Posed Problems
1.2.1 Matrices of Green’s Type
1.2.2 Existence and Uniqueness
1.2.3 Construction Procedure
1.3 Chapter Exercises
2 Spherical Surface
2.1 Basics of the Resolving Algorithm
2.2 Triangular Shaped Region
2.3 Belt-Shaped Region
2.4 Quadrilateral-Shaped Region
2.5 Robin Problem for Spherical Cap
2.6 Spherical Sector
2.7 Chapter Exercises
3 Toroidal Surface
3.1 Quadrilateral-Shaped Region
3.2 Toroidal Sector
3.3 Belt-Shaped Region
3.4 Chapter Exercises
4 Compound Structures
4.1 Matrices of Green’s Type for PDE
4.2 Compound Hemisphere
4.3 Hemisphere Joint to Cylinder
4.4 Three-Fragment Assembly
4.5 Chapter Exercises
5 Irregular Configurations
5.1 Green’s Function Version of the BIEM
5.2 Regions of Irregular Shape
5.3 Optimal Shape Design Problems

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Tags: Functions, Potential Fields, Surfaces, Yuri Melnikov