This book has comprehensively generalized analytical functions, proposed a new concept of semi-analytical functions, conjugate analytical functions and corresponding theories, and explained the application of this theory in electromagnetic fields, fluid mechanics, elastic mechanics, geometric transformation and other fields. The theory is relatively systematic and the content is novel. Because it provides a method for how to propose new concepts and how to apply new concepts, it is an important reference book for scientists engaged in theoretical research and applied development research. This book can also be used as a learning material for complex variable functions in science and engineering colleges.
PREFACE
PART I Semi-analytic Function
Chapter I Definitions and Existence Theorems
1.1 Definitions
1.2 Existence Theorems
Chapter II Principal Properties
2. 1 Algebraic and Analytic Properties
2.2 Decomposition Theorems of Complex Functions
Chapter III Physical Background and Applications
3.1 Physical Background
3.2 Applications of Semi analytic Functions
3.3 Basic Function of Complex Function
3.4 Integrul Format of Semi-analytic Function
Chapter IV Boundary Value Problem of Semi-analytic Function
PART II Conjugate Analytic Function
Chapter I Conjugate Analytic Function
1.1 Definitions
1.2 Conjugate Analytic Function and Harmonic Function
1.3 Conjugate Analytic Function and Analytic Function
1.4 Elementary Conjugate Analytic Functions
Chapter II Integral Theory of Conjugate Analytic Function
2. 1 Conjugate Integral of Complex Function
2.2 Integral Theorem
2.3 Oringinal Function and Indefinite Integral
2.4 Integral Formulas
Chapter III Series Theory of Conjugate Analytic Function
3.1 Series with Function Term
3.2 Conjugate Power Series
3.3 Series Representations
3.4 Zeros and Uniqueness Theorem
Chapter IV Isolated Points and Conjugate Power Series with
Two-direction
4.1 Conjugate Power Series with Two- direction
4.2 Isolated Singularities
4.3 Properties of Conjugate Analytic Function at
Chapter V Residue and Its Applications
5.1 Residue
5.2 The Argument Principle
Chapter VI Conjugate Analytic Extensions
6.1 Power Series Extension
6.2 Lens Arc Extension and Symmetry Principle
Chapter VII Anti-conformal Mapping
7.1 Character of Conjugate Analytic Translation
7.2 Linear Transformations
7.3 Some Element Functions
7.4 Existence Theorem and Bounded Correspondence Theorem
Chapter VIII Brief Introduction of Applications
8.1 Two-dimensional Fluid Flow
8.2 Two-dimensional Electrostatics
8.3 Two-dimensional Elastrodynamics
8.4 Applications of Anti-conformal Translation
PART III Their Tremendous Influences
Chapter I Some Properties of Bianalytic Function
1.1 Bianalytic Functions Uniqueness
1.2 Fundamental System of Bianalytic Function
Chapter II Bianalytic Function, Complex Harmonic Function and
Their Basic Boundary Value Problems
2.1 Bianalytic Functions
2.2 Complex Harmonic Functions
2.3 Basic Boundary Value Problems
Interpretation of Semi- analytic Function and Conjugate Analytic Function
References
