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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Contents

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

PART TWO

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

References 646

Subject Index 660