作者:
John B.Conway|责编:刘慧//高蓉著|John B.Conway|责编:刘慧//高蓉编|John B.Conway|责编:刘慧//高蓉译|John B.Conway|责编:刘慧//高蓉绘
出版社:世界图书出版公司
出版时间:2004-11-01
版次:1
印次:3
印刷时间:2020-01-01
页数:317
开本:24开
ISBN:9787506271912
版权提供:世界图书出版公司
作者:John B.Conway|责编:刘慧//高蓉
著:John B.Conway|责编:刘慧//高蓉
装帧:暂无
印次:3
定价:79.00
ISBN:9787506271912
出版社:世界图书出版公司
开本:24开
印刷时间:2020-01-01
语种:暂无
出版时间:2004-11-01
页数:317
外部编号:30934946
版次:1
成品尺寸:暂无
Preface for the Second Edition Preface Contents, Volume Ⅱ Ⅰ.The Complex Number System §1.The real numbers §2.The field of complex numbers §3.The complex plane §4.Polar representation and roots of complex numbers §5.Lines and half planes in the complex plane §6.The extended plane and its spherical representation Ⅱ.Metric Spaces and the Topology of C §1.Definition and examples of metric spaces §2.Connectedness §3.Sequences and comleess §4.Compactness §5.Continuity §6.Uniform convergence Ⅲ.Elementary Properties and Examples of Analytic Functions §1.Power series §2.Analytic functions §3.Analytic functions as mappings, Mobius transformations Ⅳ.Complex Integration §1.Riemann-Stieltjes integrals §2.Power series representation of analytic functions §3.Zeros of an analytic function §4.The index of a closed curve §5.Cauchy's Theorem and Integral Formula §6.The homotopic version of Cauchy's Therorem and simple connectivity §7.Counting zeros; the Open Mapping Theorem §8.Goursat's Theorem Ⅴ.Singularities §1.Classification of singularities §2.Residues §3.The Argument Principle Ⅵ.The Maximum Modulus Theorem §1.The Maximum Principle §2.Schwarz's Lemma §3.Convex functions and Hadamard's Three Circles Theorem §4.Phragmen-Lindelof Theorem Ⅶ.Compactness and Convergence in the Space of Analytic Functions §1.The space of continuous functions C (G, Ω) §2.Spaces of analytic functions §3.Spaces of meromorphic functions §4.The Riemann Mapping Theorem §5.Weierstrass Factorization Theorem §6.Factorization of the sine function §7.The gamma function §8.The Ricmann zeta function Ⅷ.Runge's Theorem §1.Runge's Theorem §2.Simple connectedness §3.Mittag-Leffler's Theorem Ⅸ.Analytic Continuation and Riemann Surfaces §1.Schwarz Reflection Principle §2.Analytic Continuation Along A Path §3.Monoy Theorem §4.Topological Spaces and Neiorhood Systems §5.The Sheaf of Germs of Analytic Functions on an Open Set §6.Analytic ManifoIds §7.Covering spaces Ⅹ.Harmonic Functions §1.Basic Properties of harmonic functions §2.Harmonic functions on a disk §3.Subharmonic and SUPerharmonic functions §4.The Dirichlet Problem §5.Gregn's Functions Ⅺ.Entire Functions §1.Jensen's Formula §2.The genus and order of an entire function §3.Hadamard Factorization Theorem Ⅻ.The Range of an Analytic Function §1.Bloch's Theorem §2.The Little Picard Theorem §3.Schottky's Theorem §4.The Great Picard Theorem Appendix A: Calculus for Complex Valued Functions on an Interval Appendix B: Suggestions for Further Study and Bibliographical Notes References Index List of Symbols