Differential Equations and Dynamical Systems (Texts in Applied Mathematics)

Differential Equations and Dynamical Systems (Texts in Applied Mathematics) by L. Perko

Title: Differential Equations and Dynamical Systems (Texts in Applied Mathematics)
Author: L. Perko
ISBN10: 3540947787
ISBN13: 978-3540947783
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K (September 30, 1996)
Language: -
Subcategory: Ordinary Differential Equations (MIT Press)
Size PDF: 1786 kb
Size Fb2: 1617 kb
Rating: 5.0/5
Votes: 265
Pages: 540 pages
Other Format: lrf doc mobi doc

Differential Equations and Dynamical Systems (Texts in Applied Mathematics) by L. Perko


pdf epub fb2 djvu



This book contains a systematic study of autonomous systems of ordinary differential equations and dynamical systems. It begins with a thorough treatment of linear systems; however, the main topic of the book is local and global behaviour of nonlinear systems. The main purpose of the book is to introduce students to the qualitative and geometric theory of ordinary differential equations originated at the end of the 19th century. It is also intended as a reference book for mathematicians doing research on dynamical systems. There are several new features in this book such as the simplified proof of the HartmanGrobman Theorem and examples illustrating the proof, map in the theory of limit cycles, an efficient method for obtaining the global phase portrait of two-dimensional systems, and the description of the behaviour of a one-parameter family of limit cycles. Readers of this book will find that, except for certain topics of current mathematical research such as the number of limit cycles and the nature of attracting sets of dynamical systems, the global qualitative theory of a nonlinear dynamical system leads to an understanding of the solution set of the nonlinear system that rivals the understanding what we have of linear flows. This textbook on control/systems theory and ordinary differential equations is intended for mathematicians and physicists.