In this post, we will see the book Generalized Analytic Functions by I. Vekua.
About the book
THIS book is concerned with foundations of the general theory of generalized analytic functions and some applications to problems of differential geometry and theory of shells.The book is intended for students of advanced courses of the mechanico-mathematical faculties, postgraduates, and likewise for research workers.
The book was translated from Russian by Ian N. Sneddon and was published in 1962.
Credits to original uploader.
You can get the book here.
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FOUNDATIONS OF THE GENERAL THEORY
OF GENERALIZED ANALYTIC FUNCTIONS
AND BOUNDARY VALUE PROBLEMS 1
Chapter 1. Some classes of functions and operators 5
Chapter 2. Reduction of a positive differential quadratic form to the canonical form. Beltrami’s equation. Geometric applications 76
Chapter 3. Foundations of General Theory of Generalized Analytic Functions 132
Chapter 4. Boundary Value Problems 221
Appendix to Chapter 4 366
SOME APPLICATIONS TO PROBLEMS OF THE THEORY OF SURFACES AND THE MEMBRANE THEORY OF SHELLS 390
Chapter 5. Foundations of the General Theory of Infinitesimal Bendings of Surfaces 391
Chapter 6. Problems of the membrane theory of shells 563
Subject Index 660