Bücher von Ferdinand Verhulst

This primer on averaging theorems provides a practical toolbox for applied mathematicians, physicists, and engineers seeking to apply the well-known mathematical theory to real-world problems. With a focus on practical applications, the book introduces new approaches to dissipative and Hamiltonian resonances and approximations on timescales longer than 1/¿.Accessible and clearly written, the book includes numerous examples ranging from elementary to complex, making it an excellent basic reference for anyone interested in the subject. The prerequisites have been kept to a minimum, requiring only a working knowledge of calculus and ordinary and partial differential equations (ODEs and PDEs).In addition to serving as a valuable reference for practitioners, the book could also be used as a reading guide for a mathematics seminar on averaging methods. Whether you're an engineer, scientist, or mathematician, this book offers a wealth of practicaltools and theoretical insights to help you tackle a range of mathematical problems.

Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences is the main focus of this workbook. In a systematic introductory manner, this unique book deliniates boundary layer theory for ordinary and partial differential equations, multi-timescale phenomena for nonlinear oscillations, diffusion and nonlinear wave equations. The book provides analysis of simple examples in the context of the general theory, as well as a final discussion of the more advanced problems. Precise estimates and excursions into the theoretical background makes this workbook valuable to both the applied sciences and mathematics fields. As a bonus in its last chapter the book includes a collection of rare and useful pieces of literature, such as the summary of the Perturbation theory of Matrices.Detailed illustrations, stimulating examples and exercises as well as a clear explanation of the underlying theory makes this workbook ideal for senior undergraduate and beginning graduate students in applied mathematics as well as science and engineering fields.

In den Niederlanden erscheint seit etwa zehn Jahren die erfolgreiche "e;Zebra-Reihe"e;, 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 Leser werden zudem angeregt, durch eigene Aktivitat mehr zu erfahren; es stehen dazu auch Internet-basierte Materialien bereit.Studierende des Lehramts Mathematik werden in diesem Buch eine wertvolle Quelle fur die fachdidaktische und wie auch die fachwissenschaftliche Ausbildung finden. Die Vielfalt der Themen und ihre attraktive Aufbereitung wird Schuler und mathematisch interessierte Laien ansprechen.

In this, the first English biography of the French mathematician and physicist, his unique achievements in these subjects are laid out alongside fascinating and revealing details such as brief overviews of his links with the other scientists he encountered.

Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a revision of the first edition of the averaging book. Updated chapters represent new insights in averaging and offer an effective entrance into this topic.

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.