Graduate courses on different aspects of numerical analysis
Boundary element methods
(Spanish). By Ricardo Celorrio & Francisco-Javier
Sayas. This is the revised version of the class notes
for the 9th Spanish-French Autumn School on Numerical
Simulation in Physics and Engineering, held in Laredo in
September 2000. It's a 107 page long course on
numerical analysis of Boundary Elements.
Domain decomposition methods (Spanish). By Salim Meddahi & Francisco-Javier Sayas. These are the classnotes of a course taught by Salim Meddahi at the University of Zaragoza in 1995.
Introduction to the Boundary Element Method. A case study: Helmholtz equation. Classnotes of a summer course taught by me at the University of Concepción (Chile) in January 2006.
A gentle introduction to the Finite Element Method. Classnotes from one of my graduate courses on FEM at the University of Zaragoza updated for a similar course at UD. Mathematically very light and with an emphasis on algorithms.
Mathematical Models in Mechanics (Spanish). A basic course on PDEs, written with students of computational mechanics in mind.
Advanced Finite Elements (Spanish). Insisting again on algorithms, but now learning about mixed, non-conforming, etc, etc.
First Steps in the Boundary Element Method. Most recently used to give students a taste of BEM after a healthy portion of FEM.
From Raviart-Thomas to HDG: a personal voyage. Adapted from a course prepared for Cádiz Numérica 2013, Cádiz, Spain.
Retarded Potentials and Time Domain Boundary Integral Equations: a road-map. The notes that led to the number 1 best seller!
Convolution Quadrature for Wave Simulations. By Matthew Hassell & Francisco-Javier Sayas. These are notes that were prepared for a course which I taught at the XVI Jacques-Louis Lions Spanish-French School on Numerical Simulation in Physics and Engineering in Pamplona, Spain. It is again focused more on algorithms.
The Jordan form
(Spanish). Matrix aspects of the construction of the
Jordan form, existence and some related combinatorial
Reorganization of information in matrices (Spanish). From rank one matrices to the singular value decomposition (Elementary)
Minimum energy solutions to ill-conditioned systems. Sometimes systems can be really badly conditioned. What to do. (Elementary)
Static and dynamic recursive least-squares. A statistical-free introduction to Kalman filters. Uses only elementary concepts of matrix analysis and numerical methods. (Elementary/Medium)
Krylov spaces, GMRES, singular values and equations of the second kind. Some results on the theory of GMRES on Hilbert spaces, focused on equations of the second kind. (Advanced)