These notes were born as a way to keep track of the contents I intended to show in a course on Advanced Topics for Mathematical Engineering at Pontificia Universidad Católica de Chile, the second semester of 2024. The idea of the course is to give a modern set of tools for a rigorous computational scientist, so that they can understand the complexity of a given problem and squeeze the most mathematics out of a problem whenever possible. This should help in developing efficient numerical methods and robust strategies to be able to trust the computational pipelines that they propose.
For contributions, please follow the format of the manuscript, which should be fairly common mathematical notation.
- Create vectors, matrices, and tensors with
\vec,\mat, and\ten. - Vector norms (and semi-norms) are
$|\cdot|$ . Function and operator norms are$\lVert \cdot \rVert$ . - Duality pairings and inner products are
$\langle \cdot, \cdot\rangle$ - Small sections can be introduced with
\paragraphinstead of a\subsubsubsubsubsubsubsubsubsubsection.
Contributors may be added as editors upon request. Otherwise, pull requests are both encouraged and desired. Thanks in advance for the help in making these notes clear and useful :) .
I have been writing most things in a rush, so help in finding typos and mistakes will be much appreciated. Raise it either by email (nicolas.barnafi at uc.cl) or directly here as an issue. Using git for everything is a personal pathology.