Introduction To Differential Equations With Dynamical Systems
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Introduction to Differential Equations with Dynamical Systems
Author: Stephen L. Campbell
language: en
Publisher: Princeton University Press
Release Date: 2008-04-21
Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length.
Ordinary Differential Equations and Dynamical Systems
Author: Thomas C. Sideris
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-10-17
This book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis and linear algebra. The presentation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. The first half of the book is devoted to the development of the basic theory: linear systems, existence and uniqueness of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigm for evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics. A common thread throughout the second part is the use of the implicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as the bridge between the two halves of the book.
Introduction to Differential Equations and Dynamical Systems
Author: Richard E. Williamson
language: en
Publisher: McGraw-Hill Science, Engineering & Mathematics
Release Date: 2001
This text is intended for use in a course in differential equations for student of pure and applied mathematics, the physical sciences, and engineering. The text is designed to be extremely flexible and includes both theory and applications. The text has been written and designed so that the applications can be covered or omitted without a loss of continuity of core topics. The odd-numbered chapters of the book cover the core theory of differential equations with basic applications, while the even-numbered chapters include extended applications from engineering and the physical sciences. In addition, the text includes optional coverage of dynamical systems. Where appropriate, the author has integrated technology into the text, primarily in the exercise sets. Chapters 2, 4, and 6 also include Computing Supplement Sections that are devoted to using numerical methods to solve differential equations.