[English]
Teknillinen Korkeakoulu
Matematiikan Laitos
opetus
Huom! Tämä sivu on vanhentunut. Kurssitiedot löytyvät syksystä 2008 alkaen Nopasta. |
Kirja: Govaerts, Willy J. F. Numerical Methods for Bifurcations of Dynamical Equilibria SIAM, 2000. |
This book describes numerical methods for detection, computation, and continuation
of equilibria and bifurcation points of equilibria of dynamical systems. In the
enormous field of differential equations this is a modest subfield with the particular
attraction of having many links with other research fields, in particular the
geometric theory of differential equations, numerical analysis, and linear algebra.
The problems that are studied arise in other sciences (physics, chemistry, biology,
engineering, economy) and so have interest in their own.
On the other hand, the numerical problems in dynamical systems theory have often influenced developments in numerical linear algebra and in numerical analysis.
Another link is with software development. The only realistic way to make numerical methods widely available is to include them in software. Much work in this direction has been done, and implementation of many of the algorithms discussed in this book are freely available.
This book is meant for those who want to apply numerical methods to bifurcation and dynamical systems problems. It is assumed that the reader is familiar with the basic techniques in analysis, numerical analysis, and linear algebra as they are usually taught in undergraduate courses in science and engineering; some reference to standard textbooks on these topics may be necessary.
Luentoja on yhteensä kahdeksan viikkoa. Harjoituksissa käsitellään tehtäviä, joista kaksi viikossa on kotitehtäviä. Kurssin lopussa pidetään tentti, johon saa lasketuista kotitehtävistä hyvityspisteitä.
Joidenkin tehtävien ratkaisuun käytetään Matlabin Matcont työkalupakettia, jonka käyttöön tutustutaan tarkemmin harjoituksissa, joten Matlab-osaamisesta on hyötyä.