Complex analysis

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Complex analysis / Eberhard Freitag, Rolf Busam

版:

2nd ed

資料種別:

図書

出版情報:

Berlin : Springer, c2009

形態:

x, 532 p. ; 24 cm

シリーズ名:

Universitext <BA00021004>

著者名:

ISBN:

9783540939825 [3540939822] (: [pbk.])

書誌ID:

BA89877901

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

その他の標題:

Funktionentheorie I

注記:

Includes bibliographical references (p. [509]-517) and index

主題:

Functions of complex variables; Functions of complex variables--Problems, exercises, etc

言語:

英語

目次情報:

Differential Calculus in the Complex Plane C / I：

Complex Numbers / I.1：

Convergent Sequences and Series / I.2：

Continuity / I.3：

Complex Derivatives / I.4：

The Cauchy-Riemann Differential Equations / I.5：

Integral Calculus in the Complex Plane C / II：

Complex Line Integrals / II.1：

The Cauchy Integral Theorem / II.2：

The Cauchy Integral Formulas / II.3：

Sequences and Series of Analytic Functions, the Residue Theorem / III：

Uniform Approximation / III.1：

Power Series / III.2：

Mapping Properties of Analytic Functions / III.3：

Singularities of Analytic Functions / III.4：

Laurent Decomposition / III.5：

Appendix to III.4 and III.5 / A：

The Residue Theorem / III.6：

Applications of the Residue Theorem / III.7：

Construction of Analytic Functions / IV：

The Gamma Function / IV.1：

The Weierstrass Product Formula / IV.2：

The Mittag-Leffler Partial Fraction Decomposition / IV.3：

The Riemann Mapping Theorem / IV.4：

Appendix : The Homotopical Version of the Cauchy Integral Theorem

Appendix : A Homological Version of the Cauchy Integral Theorem / B：

Appendix : Characterizations of Elementary Domains / C：

Elliptic Functions / V：

Liouville's Theorems / V.1：

Appendix to the Definition of the Period Lattice

The Weierstrass $$-function / V.2：

The Field of Elliptic Functions / V.3：

Appendix to Sect. V.3 : The Torus as an Algebraic Curve

The Addition Theorem / V.4：

Elliptic Integrals / V.5：

Abel's Theorem / V.6：

The Elliptic Modular Group / V.7：

The Modular Function j / V.8：

Elliptic Modular Forms / VI：

The Modular Group and Its Fundamental Region / VI.1：

The k/12-formula and the Injectivity of the j-function / VI.2：

The Algebra of Modular Forms / VI.3：

Modular Forms and Theta Series / VI.4：

Modular Forms for Congruence Groups / VI.5：

Appendix to VI.5 : The Theta Group

A Ring of Theta Functions / VI.6：

Analytic Number Theory / VII：

Sums of Four and Eight Squares / VII.1：

Dirichlet Series / VII.2：

Dirichlet Series with Functional Equations / VII.3：

The Riemann ?-function and Prime Numbers / VII.4：

The Analytic Continuation of the ?-function / VII.5：

A Tauberian Theorem / VII.6：

Solutions to the Exercises / VIII：

Solutions to the Exercises of Chapter I / VIII.1：

Solutions to the Exercises of Chapter II / VIII.2：

Solutions to the Exercises of Chapter III / VIII.3：

Solutions to the Exercises of Chapter IV / VIII.4：

Solutions to the Exercises of Chapter V / VIII.5：

Solutions to the Exercises of Chapter VI / VIII.6：

Solutions to the Exercises of Chapter VII / VIII.7：

References

Symbolic Notations

Differential Calculus in the Complex Plane C / I：

Complex Numbers / I.1：

Convergent Sequences and Series / I.2：

Continuity / I.3：

Complex Derivatives / I.4：

The Cauchy-Riemann Differential Equations / I.5：

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