Complex Analysis with MATHEMATICA

Complex Analysis with Mathematica offers a new 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.

ISBN 0521836263   Pages 598 ISBN13 9780521836265 (What's this?)   Volumes 1 Publisher Cambridge University Press   Weight (grammes) 1353 Imprint Cambridge University Press   Published in Cambridge Format Hardback   Height (mm) 247 Publication date 20 Apr 2006   Width (mm) 174 Library of Congress QA   Spine width (mm) 33 DEWEY 515.90285536   Academic level Professional / Scholarly DEWEY edition DC22

1		Why you need complex numbers		1
2		Complex algebra and geometry		10
3		Cubics, quartics and visualization of complex roots		41
4		Newton-Raphson iteration and complex fractals		56
5		A complex view o the real logistic map		78
6		The Mandelbrot set		105
7		Symmetric chaos in the complex plane		138
8		Complex functions		159
9		Sequences, series and power series		194
10		Complex differentiation		208
11		Paths and complex integration		237
12		Cauchy's theorem		248
13		Cauchy's integral formula and its remarkable consequences		263
14		Laurent series, zeroes, singularities and residues		278
15		Residue calculus : integration, summation and the argument principle		302
16		Conformal mapping I : simple mappings and Mobius transforms		338
17		Fourier transforms		357
18		Laplace transforms		381
19		Elementary applications to two-dimensional physics		401
20		Numerical transform techniques		433
21		Conformal mapping II : the Schwarz-Christoffel mapping		451
22		Tiling the Euclidean and hyperbolic planes		473
23		Physics in three and four dimensions I		513
24		Physics in three and four dimensions II		540

'William Shaw's Complex Analysis with Mathematica is a remarkable achievement. It masterfully combines excellent expositions of the beauties and subtlety of complex analysis, and several of its applications to physical theory, with clear explanations of the flexibility and the power of Mathematica for computing and for generating marvellous graphical displays.' Roger Penrose, University of Oxford 'This is an innovative text in which the basic ideas of complex analysis are skillfully interwoven with geometry, chaos and physics through the learning and repeated application of Mathematica. This text moves from complex numbers, quadratic and cubic equations through to the Schwarz-Christoffel transformation and four-dimensional physics, and at each stage promotes understanding through geometric intuition and reader participation. It should appeal to anyone with an interest in the geometric side of complex analysis.' Alan F. Beardon, University of Cambridge 'This book provides an inspiring way to learn complex analysis thanks to the inclusion of many topics of current interest in the field as well as the integration of highly visual Mathematica routines throughout. The book is sure to excite students about the field.' Bob Devaney, Boston University 'The book is far more than a standard course of complex analysis or a guide to Mathematica(r) tools.' EMS Newsletter

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