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図書
図書
1. Complex analysis. 2nd ed
Joseph Bak, Donald J. Newman
出版情報: New York : Springer-Verlag, c1997  x, 294 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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2.

図書
図書
2. Complex analysis. 3rd ed
Joseph Bak, Donald J. Newman
出版情報: New York : Springer, c2010  xii, 328 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Preface to the Third Edition
Preface to the Second Edition
The Complex Numbers / 1：
Introduction
The Field of Complex Numbers / 1.1：
The Complex Plane / 1.2：
The Solution of the Cubic Equation / 1.3：
Topological Aspects of the Complex Plane / 1.4：
Stereographic Projection; The Point at Infinity / 1.5：
Exercises
Functions of the Complex Variable z / 2：
Analytic Polynomials / 2.1：
Power Series / 2.2：
Differentiability and Uniqueness of Power Series / 2.3：
Analytic Functions / 3：
Analyticity and the Cauchy-Riemann Equations / 3.1：
Line Integrals and Entire Functions / 3.2：
Properties of the Line Integral / 4.1：
The Closed Curve Theorem for Entire Functions / 4.2：
Properties of Entire Functions / 5：
The Cauchy Integral Formula and Taylor Expansion for Entire Functions / 5.1：
Liouville Theorems and the Fundamental Theorem of Algebra; The Gauss-Lucas Theorem / 5.2：
Newton's Method and Its Application to Polynomial Equations / 5.3：
Properties of Analytic Functions / 6：
The Power Series Representation for Functions Analytic in a Disc / 6.1：
Analytic in an Arbitrary Open Set / 6.2：
The Uniqueness, Mean-Value, and Maximum-Modulus Theorems; Critical Points and Saddle Points / 6.3：
Further Properties of Analytic Functions / 7：
The Open Mapping Theorem; Schwarz' Lemma / 7.1：
The Converse of Cauchy's Theorem: Morera's Theorem; The Schwarz Reflection Principle and Analytic Arcs / 7.2：
Simply Connected Domains / 8：
The General Cauchy Closed Curve Theorem / 8.1：
The Analytic Function log z / 8.2：
Isolated Singularities of an Analytic Function / 9：
Classification of Isolated Singularities; Riemann's Principle and the Casorati-Weierstrass Theorem / 9.1：
Laurent Expansions / 9.2：
The Residue Theorem / 10：
Winding Numbers and the Cauchy Residue Theorem / 10.1：
Applications of the Residue Theorem / 10.2：
Applications of the Residue Theorem to the Evaluation of Integrals and Sums / 11：
Evaluation of Definite Integrals by Contour Integral Techniques / 11.1：
Application of Contour Integral Methods to Evaluation and Estimation of Sums / 11.2：
Further Contour Integral Techniques / 12：
Shifting the Contour of Integration / 12.1：
An Entire Function Bounded in Every Direction / 12.2：
Introduction to Conformal Mapping / 13：
Conformal Equivalence / 13.1：
Special Mappings / 13.2：
Schwarz-Christoffel Transformations / 13.3：
The Riemann Mapping Theorem / 14：
Conformal Mapping and Hydrodynamics / 14.1：
Mapping Properties of Analytic Functions on Closed Domains / 14.2：
Maximum-Modulus Theorems for Unbounded Domains / 15：
A General Maximum-Modulus Theorem / 15.1：
The Phragmén-Lindelöf Theorem / 15.2：
Harmonic Functions / 16：
Poisson Formulae and the Dirichlet Problem / 16.1：
Liouville Theorems for Re f; Zeroes of Entire Functions of Finite Order / 16.2：
Different Forms of Analytic Functions / 17：
Infinite Products / 17.1：
Analytic Functions Defined by Definite Integrals / 17.2：
Analytic Functions Defined by Dirichlet Series / 17.3：
Analytic Continuation; The Gamma and Zeta Functions / 18：
Analytic Continuation of Dirichlet Series / 18.1：
The Gamma and Zeta Functions / 18.3：
Applications to Other Areas of Mathematics / 19：
A Variation Problem / 19.1：
The Fourier Uniqueness Theorem / 19.2：
An Infinite System of Equations / 19.3：
Applications to Number Theory / 19.4：
An Analytic Proof of The Prime Number Theorem / 19.5：
Answers
References
Appendices
Index
Preface to the Third Edition
Preface to the Second Edition
The Complex Numbers / 1：
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