Mat-1.3658 Special course in numerical analysis

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.