Complex analysis with Mathematica [E-Book] / William T. Shaw.
Shaw, William T, (author)
Cambridge : Cambridge University Press, 2006
1 online resource (xxv, 571 pages)
Full Text
Table of 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.