Functions of one complex variable / John B. Conway.
Series Graduate texts in mathematics ; 11Editor: New York : Springer-Verlag, c1978Edición: 2nd edDescripción: xiii, 317 p. : il. ; 25 cmISBN: 0387903283Tema(s): Functions of complex variablesOtra clasificación: 30-01I. The Complex Number System §1. The real numbers [1] §2. The field of complex numbers [1] §3. The complex plane [3] §4. Polar representation and roots of complex numbers [4] §5. Lines and half planes in the complex plane [6] §6. The extended plane and its spherical representation [8] II. Metric Spaces and the Topology of C §1. Definition and examples of metric spaces [11] §2. Connectedness [14] §3. Sequences and completeness [17] §4. Compactness [20] §5. Continuity [24] §6. Uniform convergence [28] III. Elementary Properties and Examples of Analytic Functions §1. Power series [30] §2. Analytic functions [33] §3. Analytic functions as mappings, Möbius transformations [44] IV. Complex Integration §1. Riemann-Stieltjes integrals [58] §2. Power series representation of analytic functions [68] §3. Zeros of an analytic function [76] §4. The index of a closed curve [80] §5. Cauchy’s Theorem and Integral Formula [83] §6. The homotopic version of Cauchy’s Theorem and simple connectivity [87] §7. Counting zeros; the Open Mapping Theorem [97] §8. Goursat’s Theorem [100] V. Singularities §1. Classification of singularities [103] §2. Residues [112] §3. The Argument .Principle [123] VI. The Maximum Modulus Theorem §1. The Maximum Principle [128] §2. Schwarz’s Lemma [130] §3. Convex functions and Hadamard’s Three Circles Theorem [133] §4. Phragmen-Lindelöf Theorem [138] VII. Compactness and Convergence in the Space of Analytic Functions §1. The space of continuous functions C(G,Ω) [142] §2. Spaces of analytic functions [151] §3. Spaces of meromorphic functions [155] §4. The Riemann Mapping Theorem [160] §5. Weierstrass Factorization Theorem [164] §6. Factorization of the sine function [174] §7. The gamma function [176] §8. The Riemann zeta function [187] VIII. Runge's Theorem §1. Runge’s Theorem [195] §2. Simple connectedness [202] §3. Mittag-Leffler’s Theorem [204] IX. Analytic Continuation and Riemann Surfaces §1. Schwarz Reflection Principle [210] §2. Analytic Continuation Along A Path [213] §3. Mondromy Theorem [217] §4. Topological Spaces and Neighborhood Systems [221] §5. The Sheaf of Germs of Analytic Functions on an Open Set [227] §6. Analytic Manifolds [233] §7. Covering spaces [245] X. Harmonic Functions §1. Basic Properties of harmonic functions [252] §2. Harmonic functions on a disk [256] §3. Subharmonic and superharmonic functions [263] §4. The Dirichlet Problem [269] §5. Green's Functions [275] XI. Entire Functions $1. Jensen’s Formula [280] §2. The genus and order of an entire function [282] §3. Hadamard Factorization Theorem [287] XII. The Range of an Analytic Function §1. Bloch’s Theorem [292] §2. The Little Picard Theorem [296] §3. Schottky’s Theorem [297] §4. The Great Picard Theorem [300] Appendix A: Calculus for Complex Valued Functions on an Interval [303] Appendix B: Suggestions for Further Study and Bibliographical Notes [307]
| Item type | Home library | Shelving location | Call number | Materials specified | Copy number | Status | Date due | Barcode | Course reserves |
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Bibliografía: p. 311-312.
I. The Complex Number System --
§1. The real numbers [1] --
§2. The field of complex numbers [1] --
§3. The complex plane [3] --
§4. Polar representation and roots of complex numbers [4] --
§5. Lines and half planes in the complex plane [6] --
§6. The extended plane and its spherical representation [8] --
II. Metric Spaces and the Topology of C --
§1. Definition and examples of metric spaces [11] --
§2. Connectedness [14] --
§3. Sequences and completeness [17] --
§4. Compactness [20] --
§5. Continuity [24] --
§6. Uniform convergence [28] --
III. Elementary Properties and Examples of Analytic Functions --
§1. Power series [30] --
§2. Analytic functions [33] --
§3. Analytic functions as mappings, Möbius transformations [44] --
IV. Complex Integration --
§1. Riemann-Stieltjes integrals [58] --
§2. Power series representation of analytic functions [68] --
§3. Zeros of an analytic function [76] --
§4. The index of a closed curve [80] --
§5. Cauchy’s Theorem and Integral Formula [83] --
§6. The homotopic version of Cauchy’s Theorem and --
simple connectivity [87] --
§7. Counting zeros; the Open Mapping Theorem [97] --
§8. Goursat’s Theorem [100] --
V. Singularities --
§1. Classification of singularities [103] --
§2. Residues [112] --
§3. The Argument .Principle [123] --
VI. The Maximum Modulus Theorem --
§1. The Maximum Principle [128] --
§2. Schwarz’s Lemma [130] --
§3. Convex functions and Hadamard’s Three Circles Theorem [133] --
§4. Phragmen-Lindelöf Theorem [138] --
VII. Compactness and Convergence in the Space of Analytic Functions --
§1. The space of continuous functions C(G,Ω) [142] --
§2. Spaces of analytic functions [151] --
§3. Spaces of meromorphic functions [155] --
§4. The Riemann Mapping Theorem [160] --
§5. Weierstrass Factorization Theorem [164] --
§6. Factorization of the sine function [174] --
§7. The gamma function [176] --
§8. The Riemann zeta function [187] --
VIII. Runge's Theorem --
§1. Runge’s Theorem [195] --
§2. Simple connectedness [202] --
§3. Mittag-Leffler’s Theorem [204] --
IX. Analytic Continuation and Riemann Surfaces --
§1. Schwarz Reflection Principle [210] --
§2. Analytic Continuation Along A Path [213] --
§3. Mondromy Theorem [217] --
§4. Topological Spaces and Neighborhood Systems [221] --
§5. The Sheaf of Germs of Analytic Functions on an Open Set [227] --
§6. Analytic Manifolds [233] --
§7. Covering spaces [245] --
X. Harmonic Functions --
§1. Basic Properties of harmonic functions [252] --
§2. Harmonic functions on a disk [256] --
§3. Subharmonic and superharmonic functions [263] --
§4. The Dirichlet Problem [269] --
§5. Green's Functions [275] --
XI. Entire Functions --
$1. Jensen’s Formula [280] --
§2. The genus and order of an entire function [282] --
§3. Hadamard Factorization Theorem [287] --
XII. The Range of an Analytic Function --
§1. Bloch’s Theorem [292] --
§2. The Little Picard Theorem [296] --
§3. Schottky’s Theorem [297] --
§4. The Great Picard Theorem [300] --
Appendix A: Calculus for Complex Valued Functions on an Interval [303] --
Appendix B: Suggestions for Further Study and Bibliographical Notes [307] --
MR, 80c:30003
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