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Title

Complex Analysis with Mathematica
Author

William T. Shaw
Organization: King's College, University of London
Department: Department of Mathematics
URL: http://www.mth.kcl.ac.uk/staff/w_shaw.html
Book information

Publisher: Cambridge University Press (United Kingdom)
Copyright year: 2006
ISBN: 0521836263
Medium: Hardcover
Includes: CD-ROM
Pages: 598
Out of print?: N
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Contents

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 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 | Bibliography
Description

This book presents complex numbers in a state-of-the-art computational environment. Its innovative approach also offers insights into areas too often neglected in a student treatment, including complex chaos, mathematical art, physics in three or more dimensions, and advanced fluid dynamics.

Integration with Mathematica allows topics not usually presentable on a blackboard, such as iterative equation-solving, as well as full graphical exploration of all areas covered. The included CD contains a live version of the book with all of the Mathematica code, allowing users to run computer experiments.

Teachers can utilize the book for a traditional course, with Mathematica as a tool for illustration or for checking. Readers will enjoy it for self-study and enrichment.

Downloads, tips, reviews, and other information are available at the book's web page.

Additional Mathematica 6 notebooks to accompany this book are available in the Wolfram Library Archive.
Subject

*Mathematics > Calculus and Analysis > Complex Analysis
Keywords

complex numbers, complex algebra, complex geometry, Wessel-Argand plane, DeMoivre's theorem, cubics, quartics, complex roots, root locus plots, root movies, quintic, Cayley's problem, Cobwebbing theory, bifurcation diagrams, symmetry-related bifurcation, logistic map, Mandelbrot map, stable fixed points, Escape-time algorithm, non-linear maps, Visitation denisty plots, Riemann sphere, Holey plots, checkerboard plots, complex differentiability, holomorphic functions, analytic functions, regular functions, Cauchy-Riemann equations, Ahlfors-Struble theorem, Cauchy-Goursat theorem, Liouville's theorem, Morera's theorem, Laurent series, residue theorem, mousehole contours, argument principle, Rouche's theorem, Mobius transform, Jordan's lemma, Bromwich integral, Bromwich inversion, Efros's theorem, Navier-Stokes equations, Schwarz-Christoffel transformation, Poincare disk, Minkowski space, heptagon tilings
Related items

*Mathematica 6 update for Complex Analysis with Mathematica   [in MathSource: Packages and Programs]