Complex Analysis with Mathematica

William T. Shaw

592 pages, parution le 15/05/2006

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Résumé

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.

Integration of a course on complex variables with the symbolic computation system Mathematica ¿ An introduction to twistor methods and the use of complex variables for 3 and 4 dimensional problems. Integration of a course on complex variables with Mathematica software, supported by the accompanying CD

Sommaire

Why 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 augment principle
Conformal mapping I: simple mappings and Mobius transforms
Fourier transforms
Laplace transforms
Elementary applications to two-dimensional physics
Numerical transform techniques
Conformal mapping II: the Schwarz-Christoffel transformation
Tiling the Euclidean and hyperbolic planes
Physics in three and four dimensions I
Physics in three and four dimensions II

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	William T. Shaw
Parution	15/05/2006
Nb. de pages	592
Format	18 x 25,5
Couverture	Relié
Poids	1340g
Intérieur	Noir et Blanc
EAN13	9780521836265
ISBN13	978-0-521-83626-5