Complex Analysis with Mathematica

William T. Shaw, 2006, Cambridge University Press, 598 pp., hardcover, includes CD-ROM

ISBN: 0521836263

Complex Analysis with Mathematica presents sophisticated topics on complex numbers with full graphical explorations of all areas covered. 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.

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

This book is available in the Wolfram Research bookstore.