000			03084nam a22003498i 4500
001			CR9781316036549
003			UkCbUP
005			20200124160307.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			140424s2006||||enk o ||1 0|eng|d
020			_a9781316036549 (ebook)
020			_z9780521836265 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA76.95 _b.S523 2006
082	0	4	_a515.90285536 _222
100	1		_aShaw, William T, _cDr, _eauthor.
245	1	0	_aComplex analysis with Mathematica / _cWilliam T. Shaw.
264		1	_aCambridge : _bCambridge University Press, _c2006.
300			_a1 online resource (xxv, 571 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aWhy you need complex numbers -- Complex algebra and geometry -- Cubics, quartics and visualization of complex roots -- Newton-Raphson iteration and complex fractals -- A complex view of the real logistic map -- The Mandelbrot set -- Symmetric chaos in the complex plane -- Complex functions -- Sequences, series and power series -- Complex differentiation -- Paths and complex integration -- Cauchy's theorem -- Cauchy's integral formula and its remarkable consequences -- Laurent series, zeroes, singularities and residues -- Residue calculus: integration, summation and the argument principle -- Conformal mapping I: simple mappings and Möbius transforms -- Fourier transforms -- Laplace transforms -- Elementary applications to two-dimensional physics -- Numerical transform techniques -- Conformal mapping II: The Schwarz-Christoffel mapping -- Tiling the Euclidean and hyperbolic planes -- Physics in three and four dimensions I -- Physics in three and four dimensions II.
520			_aComplex Analysis with Mathematica offers a way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn about complex numbers in a state-of-the-art computational environment. The innovative approach also offers insights into many areas too often neglected in a student treatment, including complex chaos and mathematical art. Thus readers can also use the book for self-study and for enrichment. The use of Mathematica enables the author to cover several topics that are often absent from a traditional treatment. Students are also led, optionally, into cubic or quartic equations, investigations of symmetric chaos and advanced conformal mapping. A CD is included which contains a live version of the book: in particular all the Mathematica code enables the user to run computer experiments.
630	0	0	_aMathematica (Computer file)
650		0	_aFunctions of complex variables.
650		0	_aMathematical analysis.
776	0	8	_iPrint version: _z9780521836265
856	4	0	_uhttps://doi.org/10.1017/CBO9781316036549
999			_c520794 _d520792