Complex Analysis with MATHEMATICA?
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Estimated delivery time: In stock at the publisher, but not at Prospero's office. Delivery time approx. 3-5 weeks.
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Product details:
- Publisher Cambridge University Press
- Date of Publication 20 April 2006
- ISBN 9780521836265
- Binding Hardback
- No. of pages600 pages
- Size 244x170x33 mm
- Weight 1340 g
- Language English
- Illustrations 57 b/w illus. 79 colour illus. 375 exercises 0
Categories
Short description:
This book presents a way of learning complex analysis, using Mathematica. Includes CD with electronic version of the book.
MoreLong description:
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.
'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
Table of Contents:
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.
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