Complex Analysis with MATHEMATICA®

This book presents a way of learning complex analysis, using Mathematica. Includes CD with electronic version of the book.

William T. Shaw (Author)

9780521836265, Cambridge University Press

Hardback, published 20 April 2006

600 pages, 57 b/w illus. 79 colour illus. 375 exercises
24.4 x 17 x 3.3 cm, 1.34 kg

'The book is far more than a standard course of complex analysis or a guide to Mathematica® tools.' EMS Newsletter

Complex 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.

Preface
1. Why you need complex numbers
2. Complex algebra and geometry
3. Cubics, quartics and visualization of complex roots
4. Newton-Raphson iteration and complex fractals
5. A complex view of the real logistic map
6. The Mandelbrot set
7. Symmetric chaos in the complex plane
8. Complex functions
9. Sequences, series and power series
10. Complex differentiation
11. Paths and complex integration
12. Cauchy's theorem
13. Cauchy's integral formula and its remarkable consequences
14. Laurent series, zeroes, singularities and residues
15. Residue calculus: integration, summation and the augment principle
16. Conformal mapping I: simple mappings and Mobius transforms
17. Fourier transforms
18. Laplace transforms
19. Elementary applications to two-dimensional physics
20. Numerical transform techniques
21. Conformal mapping II: the Schwarz-Christoffel transformation
22. Tiling the Euclidean and hyperbolic planes
23. Physics in three and four dimensions I
24. Physics in three and four dimensions II
Index.

Subject Areas: Mathematical & statistical software [UFM], Complex analysis, complex variables [PBKD]