Complex Analysis with MATHEMATICA

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.