000			02661 a2200277 4500
999			_c51879 _d51879
008			191219b ||||| |||| 00| 0 eng d
020			_a9781489999085
082			_a515.9 ROD
100			_aRodriguez, Rubi E.
245			_aComplex analysis: in the spirit of Lipman Bers
250			_a2nd ed.
260			_bSpringer, _c2010 _aNew York:
300			_axviii, 306p. _bpb; _c24 cm
365			_aEURO _b59.95
440			_aGraduate texts in mathematics, 0072-5285; Vol.245
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			_aMathematics
650			_aSeveral Complex Variables
650			_aAnalytic Spaces
650			_aDifferential Equations, Partial.
650			_aMathematical analysis
650			_aFunctions of a Complex Variable.
700			_aKra, Irwin
700			_aGilman, Jane P.
942			_2ddc _cTD