000			02833cam a2200397 i 4500
001			200467267
003			TR-AnTOB
005			20260205085015.0
007			ta
008			131101s2001 tu | s |||| 0 eng d
020			_a9780387216072
020			_a0387950699
020			_a9780387950693
024	7		_a10.1007/978-0-387-21607-2 _2doi
040			_aTR-AnTOB _beng _erda _cTR-AnTOB
041	0		_aeng
050	1	4	_aQA300 _b.G364 2000
090			_aQA300 _b.G364 2000
100	1		_aGamelin, Theodore W. _eauthor _9152312
245	1	0	_aComplex analysis / _cby Theodore W. Gamelin.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2001.
300			_axviii, 478 pages : _billustrations ; _c23 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	0		_aUndergraduate Texts in Mathematics ; _x0172-6056
500			_a184 illustrations.
505	0		_aFirst Part -- I The Complex Plane and Elementary Functions -- II Analytic Functions -- III Line Integrals and Harmonic Functions -- IV Complex Integration and Analyticity -- V Power Series -- VI Laurent Series and Isolated Singularities -- VII The Residue Calculus -- Second Part -- VIII The Logarithmic Integral -- IX The Schwarz Lemma and Hyperbolic Geometry -- X Harmonic Functions and the Reflection Principle -- XI Conformal Mapping -- Third Part -- XII Compact Families of Meromorphic Functions -- XIII Approximation Theorems -- XIV Some Special Functions -- XV The Dirichlet Problem -- XVI Riemann Surfaces -- Hints and Solutions for Selected Exercises -- References -- List of Symbols.
520			_aThe book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. It conists of sixteen chapters. The first eleven chapters are aimed at an Upper Division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied in the book include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces. The three geometries, spherical, euclidean, and hyperbolic, are stressed. Exercises range from the very simple to the quite challenging, in all chapters. The book is based on lectures given over the years by the author at several places, including UCLA, Brown University, the universities at La Plata and Buenos Aires, Argentina; and the Universidad Autonomo de Valencia, Spain.
650		0	_aMathematics _9234
650		0	_aMathematical analysis _91768
650		0	_aError analysis (Mathematics) _93954
710	2		_aSpringerLink (Online service) _959873
942			_2lcc _cBK
999			_c200467267 _d85479