Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics (Texts in Applied Mathematics, 50)

Verhulst, Ferdinand

Reference

Springer

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 careful detail and are illustrated with illuminating diagrams.

Averaging Methods in Nonlinear Dynamical Systems (Applied Mathematical Sciences, 59)

Murdock, James

Sanders, Jan A.

When a mechanical system has two or more coupled vibrating components, the vibration of one of the components may destabilize the motion of the others. This destabilization effect, autoparametric resonance, is a concept that has important engineering applications. This book is the first completely devoted to the subject of autoparametric resonance in an engineering context. Using the tools of nonlinear analysis, the authors show how to carry out the first crucial step of determining the regions of parameter space where the semi-trivial solution is unstable. They describe what happens in these regions and then discuss non-trivial solutions and their stability. This text will appeal to graduate students and researchers in engineering and applied mathematics.

Autoparametric Resonance in Mechanical Systems

Engineering & Transportation

Tondl, Ales

Ruijgrok, Thijs

Nabergoj, Radoslav

Engineering

Cambridge University Press

Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

Henri Poincaré: Impatient Genius

The book describes the life of Henri Poincaré, his work style and in detail most of his unique achievements in mathematics and physics. Apart from biographical details, attention is given to Poincaré'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 Poincaré's conventionalism in mathematics and his view of conventionalism in physics; the latter has a very different character. In the foundations of mathematics his position is between intuitionism and axiomatics.
One of the purposes of the book is to show how Poincaré reached his fundamentally new results in many different fields, how he thought and how one should read him. One of the new aspects is the description of two large fields of his attention: dynamical systems as presented in his book on `new methods for celestial mechanics' and his theoretical physics papers. At the same time it will be made clear how analysis and geometry are intertwined in Poincaré's thinking and work.In dynamical systems this becomes clear in his description of invariant manifolds, his association of differential equation flow with mappings and his fixed points theory. 
There is no comparable book on Poincaré, presenting such a relatively complete vision of his life and achievements. There exist some older biographies in the French language, but they pay only restricted attention to his actual work. The reader can obtain from this book many insights in the working of a very original mind while at the same time learning about fundamental results for modern science

Biographies & Memoirs

The book describes the life of Henri Poincaré, his work style and  in detail most of his unique achievements in mathematics and physics. Apart from biographical details, attention is given to Poincaré'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 Poincaré's conventionalism in mathematics and his view of conventionalism in physics; the latter has a very different character. In the foundations of mathematics his position is between intuitionism and axiomatics.One of the purposes of the book is to show how Poincaré  reached his fundamentally new results in many different fields, how he thought and  how one should read him. One of the new aspects is the description of two large fields of his attention: dynamical systems as presented  in his book on `new methods for celestial mechanics' and his theoretical physics papers. At the same time it will be made clear how analysis and geometry are intertwined in Poincaré's thinking and work.In dynamical systems this becomes clear in his description of invariant manifolds, his association of differential equation flow with mappings and his fixed points theory. There is no comparable book on Poincaré, presenting such a relatively complete vision of his life and achievements. There exist some older biographies in the French language, but they pay only restricted attention to his actual work. The reader can obtain from this book many insights in the working of a very original mind while at the same time learning about fundamental results for modern science

A Toolbox of Averaging Theorems: Ordinary and Partial Differential Equations (Surveys and Tutorials in the Applied Mathematical Sciences)

Science & Math

Mathematics

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.

Nonlinear Differential Equations and Dynamical Systems (Universitext)

See the best price to sell, buy, or rent books by Verhulst, Ferdinand. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Verhulst, Ferdinand

See the best price to sell, buy, or rent books by Verhulst, Ferdinand. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics (Texts in Applied Mathematics, 50)

Averaging Methods in Nonlinear Dynamical Systems (Applied Mathematical Sciences, 59)

Autoparametric Resonance in Mechanical Systems

Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics (Texts in Applied Mathematics, 50)

Henri Poincaré: Impatient Genius

Henri Poincaré: Impatient Genius

A Toolbox of Averaging Theorems: Ordinary and Partial Differential Equations (Surveys and Tutorials in the Applied Mathematical Sciences)

Nonlinear Differential Equations and Dynamical Systems (Universitext)