000			03665nam a22005295i 4500
001			978-0-8176-4513-7
003			DE-He213
005			20161121231030.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780817645137 _9978-0-8176-4513-7
024	7		_a10.1007/978-0-8176-4513-7 _2doi
050		4	_aQA331-355
072		7	_aPBKD _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.9 _223
100	1		_aPonnusamy, S. _eauthor.
245	1	0	_aComplex Variables with Applications _h[electronic resource] / _cby S. Ponnusamy, Herb Silverman.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2006.
300			_aXIV, 514 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aAlgebraic and Geometric Preliminaries -- Topological and Analytic Preliminaries -- Bilinear Transformations and Mappings -- Elementary Functions -- Analytic Functions -- Power Series -- Complex Integration and Cauchy’s Theorem -- Applications of Cauchy’s Theorem -- Laurent Series and the Residue Theorem -- Harmonic Functions -- Conformal Mapping and the Riemann Mapping Theorem -- Entire and Meromorphic Functions -- Analytic Continuation.
520			_aComplex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector. Examined properly, each perspective provides crucial insight into the interrelations between the complex number system and its parent, the real number system. The authors explore these relationships by adopting both generalization and specialization methods to move from real variables to complex variables, and vice versa, while simultaneously examining their analytic and geometric characteristics, using geometry to illustrate analytic concepts and employing analysis to unravel geometric notions. The engaging exposition is replete with discussions, remarks, questions, and exercises, motivating not only understanding on the part of the reader, but also developing the tools needed to think critically about mathematical problems. This focus involves a careful examination of the methods and assumptions underlying various alternative routes that lead to the same destination. The material includes numerous examples and applications relevant to engineering students, along with some techniques to evaluate various types of integrals. The book may serve as a text for an undergraduate course in complex variables designed for scientists and engineers or for mathematics majors interested in further pursuing the general theory of complex analysis. The only prerequisite is a basic knowledge of advanced calculus. The presentation is also ideally suited for self-study.
650		0	_aMathematics.
650		0	_aFunctions of complex variables.
650		0	_aApplied mathematics.
650		0	_aEngineering mathematics.
650		0	_aGeometry.
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aFunctions of a Complex Variable.
650	2	4	_aApplications of Mathematics.
650	2	4	_aSeveral Complex Variables and Analytic Spaces.
650	2	4	_aNumber Theory.
650	2	4	_aGeometry.
650	2	4	_aAppl.Mathematics/Computational Methods of Engineering.
700	1		_aSilverman, Herb. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817644574
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4513-7
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c507536 _d507536