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书名 | 半解析函数、共轭解析函数及其重大影响 |
分类 | 科学技术-建筑-水利水电 |
作者 | 王见定 |
出版社 | 中国水利水电出版社 |
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简介 | 作者简介 王见定,1981年毕业于北京工业大学数学师资班,就职于北京信息科技大学理学院,数学教授。靠前有名数学家,靠前资深统计学会会员。1981年抢先发售在世界上提出半解析函数理论,于1988年抢先发售提出并系统建立共轭解析函数理论,并将这两项理论成功地应用于电场、磁场、流体力学、弹性力学等领域。2005年王见定教授发现了社会统计学与数理统计学的内在联系和区别,从而建立了统计学的统一理论。 目录 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 内容推荐 本书将解析函数进行了全面推广,提出了半解析函数、共轭解析函数的全新概念及相应的理论,并说明了这套理论在电磁场、流体力学、弹性力学、几何变换等领域的应用。该理论比较系统,内容新颖,由于它提供了怎样提出新概念、怎样应用新概念的方法,因而对从事理论研究和应用开 |
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