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AuthorLang, Serge. author
TitleComplex Analysis [electronic resource] / by Serge Lang
ImprintNew York, NY : Springer New York : Imprint: Springer, 1999
Edition Fourth Edition
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Descript XIV, 489 p. 85 illus. online resource


The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. The first half, more or less, can be used for a one-semester course addressed to undergraduates. The second half can be used for a second semester, at either level. Somewhat more material has been included than can be covered at leisure in one or two terms, to give opportunities for the instructor to exercise individual taste, and to lead the course in whatever directions strikes the instructor's fancy at the time as well as extra readยญ ing material for students on their own. A large number of routine exerยญ cises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recommend to anyone to look through them. More recent texts have emphasized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex analysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues


One Basic Theory -- I Complex Numbers and Functions -- II Power Series -- III Cauchyโ{128}{153}s Theorem, First Part -- IV Winding Numbers and Cauchyโ{128}{153}s Theorem -- V Applications of Cauchyโ{128}{153}s integral Formula -- VI Calculus of Residues -- VII Conformal Mappings -- VIII Harmonic Functions -- Two Geometric Function Theory -- IX Schwarz Reflection -- X The Riemann Mapping Theorem -- XI Analytic Continuation Along Curves -- Three Various Analytic Topics -- XII Applications of the Maximum Modulus Principle and Jensenโ{128}{153}s Formula -- XIII Entire and Meromorphic Functions -- XIV Elliptic Functions -- XV The Gamma and Zeta Functions -- XVI The Prime Number Theorem -- ยง1. Summation by Parts and Non-Absolute Convergence -- ยง2. Difference Equations -- ยง3. Analytic Differential Equations -- ยง4. Fixed Points of a Fractional Linear Transformation -- ยง6. Cauchyโ{128}{153}s Theorem for Locally Integrable Vector Fields -- ยง7. More on Cauchy-Riemann

Mathematics Mathematical analysis Analysis (Mathematics) Mathematics Analysis


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