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 (in Spanish). 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) on January 2006.
A gentle introduction to the Finite Element Method. Classnotes from one of my graduate courses on FEM at the University of Zaragoza. Mathematically very light and with an emphasis on algorithms.
Mathematical Models in Mechanics (Spanish). A basic course on PDEs, thought for students of computational mechanics.
Advanced Finite Elements (Spanish). Insisting again on algorithms, but now learning about mixed, non-conforming, etc, etc.
Materials
Part of this needs some revision. I keep on finding typos.- The Jordan form (Spanish). Matrix aspects of the construction of the Jordan form, existence and some related combinatorial problems. [Elementary/Medium]
- 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]
What about the funny name? I'm all rotten with literature. Google Constant Lambert and you will find the hidden reference
Five mathematicians playing good old Saint-Säens at Prof. Whiteman's house (he's playing the cello) during MAFELAP2006.
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Mathematics, Ho!
is a personal
project for individual and comunal achievement in higher Maths among
Mathematicians, with a bias to Applied Mathematics. It is a collection
of classnotes and small courses. I do not claim entire originality in
these, since they have been much influenced by what I report as
references.
Conditions of use. You are allowed to use these pages and to
share this material. Most of it is by no means aimed to be given to
undergraduate students, since the style is often too dry. Anyway you
are requested to quote this as a source whenever you make extensive use
of it. Note also that this is permanently work in progress, so I might
change the version without further notice.