Shaw, William. 　著

内容

目次

Preface; 1. Why you need complex numbers; 2. Complex algebra andgeometry; 3. Cubics, quartics and visualization of complex roots; 4.Newton-Raphson iteration and complex fractals; 5. A complex view of the reallogistic map; 6. The Mandelbrot set; 7. Symmetric chaos in the complex plane;8. Complex functions; 9. Sequences, series and power series; 10. Complexdifferentiation; 11. Paths and complex integration; 12. Cauchy's theorem; 13.Cauchy's integral formula and its remarkable consequences; 14. Laurentseries, 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. Laplacetransforms; 19. Elementary applications to two-dimensional physics; 20.Numerical transform techniques; 21. Conformal mapping II: theSchwarz-Christoffel transformation; 22. Tiling the Euclidean and hyperbolicplanes; 23. Physics in three and four dimensions I; 24. Physics in three andfour dimensions II; Index.