000 03788nam a22004695i 4500
001 978-1-4419-7323-8
003 DE-He213
005 20140220082803.0
007 cr nn 008mamaa
008 121120s2013 xxu| s |||| 0|eng d
020 _a9781441973238
_9978-1-4419-7323-8
024 7 _a10.1007/978-1-4419-7323-8
_2doi
050 4 _aQA331-355
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.9
_223
100 1 _aRodríguez, Rubí E.
_eauthor.
245 1 0 _aComplex Analysis
_h[electronic resource] :
_bIn the Spirit of Lipman Bers /
_cby Rubí E. Rodríguez, Irwin Kra, Jane P. Gilman.
250 _a2nd ed. 2013.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXVIII, 306 p. 27 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v245
505 0 _aPreface to Second Edition -- Preface to First Edition -- Standard Notation and Commonly Used Symbols -- 1 The Fundamental Theorem in Complex Function Theory -- 2 Foundations -- 3 Power Series -- 4 The Cauchy Theory - A Fundamental Theorem -- 5 The Cauchy Theory - Key Consequences -- 6 Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions -- 7 Sequences and Series of Holomorphic Functions -- 8 Conformal Equivalence and Hyperbolic Geometry -- 9 Harmonic Functions -- 10 Zeros of Holomorphic Functions -- Bibliographical Notes -- Bibliography -- Index.
520 _aThis book is intended for a graduate course in complex analysis, where the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two- and three-manifolds, and number theory. Complex analysis has connections and applications to many other subjects in mathematics and to other sciences. Thus this material will also be of interest to computer scientists, physicists, and engineers. The book covers most, if not all, of the material contained in Lipman Bers’s courses on first year complex analysis. In addition, topics of current interest, such as zeros of holomorphic functions and the connection between hyperbolic geometry and complex analysis, are explored. In addition to many new exercises, this second edition introduces a variety of new and interesting topics. New features include a section on Bers's theorem on isomorphisms between rings of holomorphic functions on plane domains; necessary and sufficient conditions for the existence of a bounded analytic function on the disc with prescribed zeros; sections on subharmonic functions and Perron's principle; and a section on the ring of holomorphic functions on a plane domain.  There are three new appendices: the first is a contribution by Ranjan Roy on the history of complex analysis, the second contains background material on exterior differential calculus, and the third appendix includes an alternate approach to the Cauchy theory.
650 0 _aMathematics.
650 0 _aFunctions of complex variables.
650 1 4 _aMathematics.
650 2 4 _aFunctions of a Complex Variable.
700 1 _aKra, Irwin.
_eauthor.
700 1 _aGilman, Jane P.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441973221
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v245
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-7323-8
912 _aZDB-2-SMA
999 _c94463
_d94463