# Mathematical Methods II

Part of the Mandelbrot set.
Computed in class (edition 2013) during the "computer session" to answer Problem II of handout 7: the area of the Mandelbrot set in the region $\mathrm{Re}(z)\ge 0\approx2\times 0.2$ (the later figure is computed by pixel counting on the figure here displayed).
Homotopic transformation.
Homotopic transformation $(1-t)/z+t\exp(z)$ of the rectangular patch of $\mathbf{C}$ defined by $-3\le x\le 3$ and $0\le y\le\pi$ as function of $t$, showing how straight lines are remapped into circles of different natures in both half-planes of $\mathbf{C}$. Part of an home exam (edition 2014).