Mathematica Version 6 Compatibility Information
(continued)

This notebook continues Chapter by Chapter observations. Don't forget to look at the introduction in the first notebook!

9 Sequences, series and power series

9.5 \[MathematicaIcon] Visualization of series and functions

This is just another case of managing the colouring through the use of ColorFunction, and not turning off the lighting:

UnitCoefPowerSeries[z_, a_, N_Integer] := 
  Sum[z^k/k^a, {k, 1, N}]
  
plot[n_, ptsr_, ptsang_, trunc_] :=
  ParametricPlot3D[{r*Cos[theta], r*Sin[theta], 
    Abs[UnitCoefPowerSeries[r*Exp[I*theta], n, trunc]]},
   {r, 0.001, 0.99}, {theta, 0, 2 Pi},
   ColorFunction -> 
    (Hue[Arg[UnitCoefPowerSeries[#4*Exp[I*#5], n, trunc]]/Pi]&),
   ColorFunctionScaling -> False,
   PlotRange -> All, ViewPoint -> {-2, -2, 2}, Axes -> False,
   PlotPoints -> {ptsr, ptsang}];

Here is the second example revisited. Note the mesh is also less intrusive with the new defaults.

plot[1, 30, 60, 30]

10 Complex differentiation

10.1 Complex differentiability at a point

Nothing goes wrong here but you might want to turn up the mesh setting and try out the rotation tools.

ParametricPlot3D[{r Cos[θ], r Sin[θ], Sin[2θ]/2},
	{r, 0, 1}, {θ, 0, 2π}, PlotPoints -> {20, 40}, Mesh -> 20]

12 Cauchy's theorem

12.5 \[MathematicaIcon] Mathematica pictures of the triangle subdivision

This works OK but the edges of the triangles will disappear when viewed on-screen as a very low line thickness has been specified. If you want to see them on-screen use the following definition:

Triangle[{a_, b_, c_}] := Module[{edge = {{Re[a], Im[a]}, {Re[b], Im[b]},
			{Re[c], Im[c]}, {Re[a], Im[a]}}}, 
				{{Hue[Random[]],  Polygon[edge]}, {AbsoluteThickness[0.5], Line[edge]}}]

The rest works as in the printed text.