000			02898nmm a22002175i 4500
005			20230705150643.0
008			130107s1999 xxu| s |||| 0|eng d
020			_a9781475730838 _9978-1-4757-3083-8
082			_a515 _223
100			_aLang, Serge. _920771
245			_aComplex Analysis _h[electronic resource] / _cby Serge Lang.
250			_a4th ed. 1999.
260			_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c1999.
300			_aXIV, 489 p. 85 illus. _bonline resource.
505			_aOne Basic Theory -- I Complex Numbers and Functions -- II Power Series -- III Cauchy's Theorem, First Part -- IV Winding Numbers and Cauchy's Theorem -- V Applications of Cauchy'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 Jensen's Formula -- XIII Entire and Meromorphic Functions -- XIV Elliptic Functions -- XV The Gamma and Zeta Functions -- XVI The Prime Number Theorem -- §1. Summation by Parts and Non-Absolute Convergence -- §2. Difference Equations -- §3. Analytic Differential Equations -- §4. Fixed Points of a Fractional Linear Transformation -- §6. Cauchy's Theorem for Locally Integrable Vector Fields -- §7. More on Cauchy-Riemann.
520			_aThe 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 read­ ing material for students on their own. A large number of routine exer­ 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.
650			_aMathematical analysis. _920772
650			_aAnalysis. _920773
856			_uhttps://doi.org/10.1007/978-1-4757-3083-8
942			_cEBK
999			_c13676 _d13676