000			03848nam a22004695i 4500
001			978-1-4614-0195-7
003			DE-He213
005			20140220083732.0
007			cr nn 008mamaa
008			110629s2011 xxu| s |||| 0|eng d
020			_a9781461401957 _9978-1-4614-0195-7
024	7		_a10.1007/978-1-4614-0195-7 _2doi
050		4	_aQA331-355
072		7	_aPBKD _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.9 _223
100	1		_aAgarwal, Ravi P. _eauthor.
245	1	3	_aAn Introduction to Complex Analysis _h[electronic resource] / _cby Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas.
250			_a1.
264		1	_aBoston, MA : _bSpringer US, _c2011.
300			_aXIV, 331p. 94 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPreface.-Complex Numbers.-Complex Numbers II -- Complex Numbers III.-Set Theory in the Complex Plane.-Complex Functions.-Analytic Functions I.-Analytic Functions II.-Elementary Functions I -- Elementary Functions II -- Mappings by Functions -- Mappings by Functions II -- Curves, Contours, and Simply Connected Domains -- Complex Integration -- Independence of Path -- Cauchy–Goursat Theorem -- Deformation Theorem -- Cauchy’s Integral Formula -- Cauchy’s Integral Formula for Derivatives -- Fundamental Theorem of Algebra -- Maximum Modulus Principle -- Sequences and Series of Numbers -- Sequences and Series of Functions -- Power Series -- Taylor’s Series -- Laurent’s Series -- Zeros of Analytic Functions -- Analytic Continuation -- Symmetry and Reflection -- Singularities and Poles I -- Singularities and Poles II -- Cauchy’s Residue Theorem -- Evaluation of Real Integrals by Contour Integration I -- Evaluation of Real Integrals by Contour Integration II -- Indented Contour Integrals -- Contour Integrals Involving Multi–valued Functions -- Summation of Series. Argument Principle and Rouch´e and Hurwitz Theorems -- Behavior of Analytic Mappings -- Conformal Mappings -- Harmonic Functions -- The Schwarz–Christoffel Transformation -- Infinite Products -- Weierstrass’s Factorization Theorem -- Mittag–Leffler’s Theorem -- Periodic Functions -- The Riemann Zeta Function -- Bieberbach’s Conjecture -- The Riemann Surface -- Julia and Mandelbrot Sets -- History of Complex Numbers -- References for Further Reading -- Index.
520			_aThis textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner.   Key features of this textbook: -Effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures - Uses detailed examples to drive the presentation -Includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section -covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics -Provides a concise history of complex numbers     An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.
650		0	_aMathematics.
650		0	_aGlobal analysis (Mathematics).
650		0	_aFunctions of complex variables.
650	1	4	_aMathematics.
650	2	4	_aFunctions of a Complex Variable.
650	2	4	_aAnalysis.
700	1		_aPerera, Kanishka. _eauthor.
700	1		_aPinelas, Sandra. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461401940
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-0195-7
912			_aZDB-2-SMA
999			_c106217 _d106217