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Problems and solutions for complex analysis / Rami Shakarchi.
AUTOR:
Rami Shakarchi - Serge, Lang
ISBN:
0387988319
EDITOR:
Springer
IDIOMA:
eng
PÁGINAS:
XI, 246
AÑO:
1999
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RESUMEN
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Covers topics such as power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings, and harmonic functions. This book includes problems on Schwartz reflection, analytic continuation, Jensen's formula, the Phragmen-Lindeloef theorem, entire functions, and others.
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INDICE
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Preface
I Complex Numbers and Functions 1
II Power Series 14
III Cauchy's Theorem, First Part 36
IV Winding Numbers and Cauchy's Theorem 48
V Applications of Cauchy's Integral Formula 51
VI Calculus of Residues 76
VII Conformal Mappings 119
VIII Harmonic Functions 146
IX Schwarz Reflection 175
X The Riemann Mapping Theorem 179
XI Analytic Continuation along Curves 185
XII Applications of the Maximum Modulus Principle and Jensen's Formula 191
XIII Entire and Meromorphic Functions 206
XIV The Gamma and Zeta Functions 219
XV The Prime Number Theorem 241
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