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Contains well-chosen examples and exercises

A student-friendly introduction that follows a workbook type approach

The book describes the life of Henri Poincare, his work style and in detail most of his unique achievements in mathematics and physics. Apart from biographical details, attention is given to Poincare's contributions to automorphic functions, differential equations and dynamical systems, celestial mechanics, mathematical physics in particular the theory of the electron and relativity, topology (analysis situs). A chapter on philosophy explains Poincare's conventionalism in mathematics and his view of conventionalism in physics; the latter has a very different character. In the foundations...

For lecture courses that cover the classical theory of nonlinear differential equations associated with Poincare and Lyapunov and introduce the student to the ideas of bifurcation theory and chaos, this text is ideal. Its excellent pedagogical style typically consists of an insightful overview followed by theorems, illustrative examples, and exercises.

In den Niederlanden erscheint seit etwa zehn Jahren die erfolgreiche "Zebra-Reihe," die durch eine einzigartige Kooperation von Schulpraktikern, Mathematikdidaktikern und Fachwissenschaftlern entstanden ist. Ohne vertiefte Vorkenntnisse ermoglichen sie eigenes Erforschen und Entdecken von Mathematik.

Aus den bisher erschienenen Banden wurden fur das vorliegende Buch sechs mit Schwerpunktthema Geometrie ins Deutsche ubersetzt. Die zahlreichen Facetten der Geometrie und ihre Querverbindungen innerhalb und auerhalb der Mathematik werden in dieser Sammlung sichtbar. Die Leserinnen und...

The book describes the life of Henri Poincare, his work style and in detail most of his unique achievements in mathematics and physics. Apart from biographical details, attention is given to Poincare's contributions to automorphic functions, differential equations and dynamical systems, celestial mechanics, mathematical physics in particular the theory of the electron and relativity, topology (analysis situs). A chapter on philosophy explains Poincare's conventionalism in mathematics and his view of conventionalism in physics; the latter has a very different character. In the foundations...

Contains well-chosen examples and exercises

A student-friendly introduction that follows a workbook type approach

Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. One of the most striking features of the book is the collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in...

Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. One of the most striking features of the book is the collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in...