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 o 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 argument 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 mapping
22 Tiling the Euclidean and hyperbolic planes
23 Physics in three and four dimensions I
24 Physics in three and four dimensions II