Algebraic Analysis of Singular Perturbation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Analysis of Singular Perturbation Theory write by Takahiro Kawai. This book was released on 2005. Algebraic Analysis of Singular Perturbation Theory available in PDF, EPUB and Kindle. The topic of this book is the study of singular perturbations of ordinary differential equations, i.e., perturbations that represent solutions as asymptotic series rather than as analytic functions in a perturbation parameter. The main method used is the so-called WKB (Wentzel-Kramers-Brillouin) method, originally invented for the study of quantum-mechanical systems. The authors describe in detail the WKB method and its applications to the study of monodromy problems for Fuchsian differential equations and to the analysis of Painleve functions. This volume is suitable for graduate students and researchers interested in differential equations and special functions.
Geometric Singular Perturbation Theory Beyond the Standard Form
Geometric Singular Perturbation Theory Beyond the Standard Form - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Singular Perturbation Theory Beyond the Standard Form write by Martin Wechselberger. This book was released on 2020-02-21. Geometric Singular Perturbation Theory Beyond the Standard Form available in PDF, EPUB and Kindle. This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.
Singular Perturbation Theory
Singular Perturbation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Singular Perturbation Theory write by R.S. Johnson. This book was released on 2005-12-28. Singular Perturbation Theory available in PDF, EPUB and Kindle. The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established. The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then goes beyond this by reviewing recent contributions, and so serving as a valuable reference source. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems would otherwise have been impossible.
Methods and Applications of Singular Perturbations
Methods and Applications of Singular Perturbations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods and Applications of Singular Perturbations write by Ferdinand Verhulst. This book was released on 2006-06-04. Methods and Applications of Singular Perturbations available in PDF, EPUB and Kindle. Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
Singular Perturbation Methods for Ordinary Differential Equations
Singular Perturbation Methods for Ordinary Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Singular Perturbation Methods for Ordinary Differential Equations write by Robert E., Jr. O'Malley. This book was released on 2012-12-06. Singular Perturbation Methods for Ordinary Differential Equations available in PDF, EPUB and Kindle. This book results from various lectures given in recent years. Early drafts were used for several single semester courses on singular perturbation meth ods given at Rensselaer, and a more complete version was used for a one year course at the Technische Universitat Wien. Some portions have been used for short lecture series at Universidad Central de Venezuela, West Vir ginia University, the University of Southern California, the University of California at Davis, East China Normal University, the University of Texas at Arlington, Universita di Padova, and the University of New Hampshire, among other places. As a result, I've obtained lots of valuable feedback from students and listeners, for which I am grateful. This writing continues a pattern. Earlier lectures at Bell Laboratories, at the University of Edin burgh and New York University, and at the Australian National University led to my earlier works (1968, 1974, and 1978). All seem to have been useful for the study of singular perturbations, and I hope the same will be true of this monograph. I've personally learned much from reading and analyzing the works of others, so I would especially encourage readers to treat this book as an introduction to a diverse and exciting literature. The topic coverage selected is personal and reflects my current opin ions. An attempt has been made to encourage a consistent method of ap proaching problems, largely through correcting outer limits in regions of rapid change. Formal proofs of correctness are not emphasized.
