000			03847nam a22004695i 4500
001			978-0-387-74715-6
003			DE-He213
005			20161121231125.0
007			cr nn 008mamaa
008			100301s2007 xxu| s |||| 0|eng d
020			_a9780387747156 _9978-0-387-74715-6
024	7		_a10.1007/978-0-387-74715-6 _2doi
050		4	_aQA331-355
072		7	_aPBKD _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.9 _223
100	1		_aGilman, Jane P. _eauthor.
245	1	0	_aComplex Analysis _h[electronic resource] : _bIn the Spirit of Lipman Bers / _cby Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez.
264		1	_aNew York, NY : _bSpringer New York, _c2007.
300			_aXIV, 220 p. 20 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		_aThe Fundamental Theorem in Complex Function Theory -- Foundations -- Power Series -- The Cauchy Theory–A Fundamental Theorem -- The Cauchy Theory–Key Consequences -- Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions -- Sequences and Series of Holomorphic Functions -- Conformal Equivalence -- Harmonic Functions -- Zeros of Holomorphic Functions.
520			_aThis book is intended for a graduate course on complex analysis, also known as function theory. 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 current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and three-manifolds, and number theory. Complex analysis has connections and applications to many other subjects in mathematics and to other sciences. It is an area where the classic and the modern techniques meet and benefit from each other. This material should be part of the education of every practicing mathematician, and it will also be of interest to computer scientists, physicists, and engineers. The first part of the book is a study of the many equivalent ways of understanding the concept of analyticity. The many ways of formulating the concept of an analytic function are summarized in what is termed the Fundamental Theorem for functions of a complex variable. The organization of these conditions into a single unifying theorem with an emphasis on clarity and elegance is a hallmark of Lipman Bers's mathematical style. Here it provides a conceptual framework for results that are highly technical and often computational. The framework comes from an insight that, once articulated, will drive the subsequent mathematics and lead to new results. In the second part, the text proceeds to a leisurely exploration of interesting ramifications of the main concepts. The book covers most, if not all, of the material contained in 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.
650		0	_aMathematics.
650		0	_aFunctions of complex variables.
650	1	4	_aMathematics.
650	2	4	_aFunctions of a Complex Variable.
650	2	4	_aSeveral Complex Variables and Analytic Spaces.
700	1		_aKra, Irwin. _eauthor.
700	1		_aRodríguez, Rubí E. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387747149
830		0	_aGraduate Texts in Mathematics, _x0072-5285 ; _v245
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-74715-6
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c508938 _d508938