This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians.
The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus.
Dr. O'Malley has written a number of books on singular perturbations. This book has developedfrom many of his works in the field of perturbation theory.
|Publisher:||Springer International Publishing|
|Edition description:||Softcover reprint of the original 1st ed. 2014|
|Product dimensions:||6.10(w) x 9.25(h) x (d)|
About the Author
Table of ContentsPreface.- Ludwig Prandtl's Boundary Layer Theory.- Asymptotic Approximations.- The Method of Matches Asymptotic Expansions and Its Generalizations.- Wendepunkts and Canards (Turning Points and Delayed Bifurcations).- Two-timing, Geometric, and Multi-scale Methods.- A Simple Multi-scale Procedure for Both Oscillatory and Boundary Layer Problems.- References.- Index.
What People are Saying About This
"Such a book could be written only by an author who has devoted most of his working life to this topic, always with an eye on human interactions and the background of people in the field."
"The book is a great gift to the world of mathematical analysis."
Ferdinand Verhulst, Professor at the Mathematisch Instituut, University of Utrecht, the Netherlands, writing for SIAM May 15, 2015