# 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).

This page gathers informations and material related to my course MÉTODOS MATEMÁTICOS II at the Universidad Autónoma de Madrid.

## Lectures

The content leaves room for 3 to 5 sessions devoted to buffering the material (longer lectures), accommodating "All Questions Answered" sessions and revisiting material in need of attention before the exams.

Each lecture is accompanied by a two-hour exercises sessions. Lecture 19 is delivered as a Seminar, i.e., at a higher pace, jumping over intermediate results, no taking feedback from the audience and presenting more advanced material.