15 interactive notebooks ready to launch.
Visualize the complex plane and generate the Mandelbrot set.
Use domain coloring to understand complex function behavior visually.
Explore polynomial roots in the complex plane and unit circle symmetries.
Compute Cauchy-Riemann conditions to test holomorphicity.
Transform domains using conformal maps and visualize angle preservation.
Explore Möbius transformations and their effect on the extended complex plane.
Compute complex path integrals and understand contour orientation.
Use Cauchy’s theorem to evaluate integrals around closed contours.
Apply integral formulas to compute complex derivatives and values.
Expand complex functions in Taylor and Laurent series around singular points.
Investigate essential singularities and Picard’s great theorem visually.
Evaluate complex integrals using residues at poles.
Visualize branch cuts and how multi-valued functions become single-valued.
Explore Riemann surfaces as the natural domains of multi-valued complex functions.
Continue analytic functions beyond their original region of convergence.