Differential Equations: Theory and Applications

This book was written as a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as time-honored and important applications of this theory. His­ torically, these were the applications that spurred the development of the mathematical theory and in hindsight they are still the best applications for illustrating the concepts, ideas, and impact of the theory. While the book is intended for traditional graduate students in mathe­ matics, the material is organized so that the book can also be used in a wider setting within today's modern university and society (see "Ways to Use the Book" below). In particular, it is hoped that interdisciplinary programs with courses that combine students in mathematics, physics, engineering, and other sciences can benefit from using this text. Working professionals in any of these fields should be able to profit too by study of this text. An important, but optional component of the book (based on the in­ structor's or reader's preferences) is its computer material. The book is one of the few graduate differential equations texts that use the computer to enhance the concepts and theory normally taught to first- and second-year graduate students in mathematics. I have made every attempt to blend to­ gether the traditional theoretical material on differential equations and the new, exciting techniques afforded by computer algebra systems (CAS), like Maple, Mathematica, or Matlab.

From the reviews:

"This book is a comprehensive reader-friendly introduction to differential equations. … The theory is illustrated by a great number of nice examples, applications, figures. … the CD-ROM attachment is a powerful add-on resource for deeper studies and research. … I can warmly recommend the book for graduate mathematics, physic students and also students in applied sciences. Finally, I would like to encourage students, their professors and researchers to do computer experiments and explorations with … the CD-ROM for improving their study, teaching and scientific work." (János Karsai, Acta Scientiarum Mathematica, Vol. 70, 2004)

"The book under review is intended for a one or two semester graduate course in ordinary differential equations. A novel feature of the book is the incorporation of Maple into the presentation, and a CD-ROM of Maple worksheets that illustrate the solution method for many of the ODEs in the book. This well written book offers an application-minded instructor great flexibility in designing a course. All the necessary theory is included, as well as wide range of examples from physics and engineering … ." (J. E. Paullet, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 84 (6), 2004)

"This book is one of the few graduate differential equations texts that use the computer to enhance the concepts and theory normally taught to first- and second-year graduate students in mathematics. The author gives a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems … . This book is accompanied with a CD-ROM for some complements and supplements. Many of the pertinent examples in the text that use Maple are on the CD-ROM." (Wei Nian Zhang, Mathematical Reviews, 2002 b)

"This book is intended to serve as a comprehensive introduction to the theory of ordinary differential equations … . the material is organized so that it can be also used in a wider setting within today’s modern university and society. … The book makes every attempt to blend together the traditional theoretical material on differential equations and the new techniques afforded by computer algebra systems … . The CD-ROM contains all the electronic material for mastering and enjoying the computer component of the book." (International Aerospace Abstracts, Vol. 42 (5), 2002)

"This book is intended for first- and second-year graduate students in mathematics and also organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering. … The book is well written and provides many interesting examples. The author gives a comprehensive introduction to the theory on ordinary differential equations with a focus on mechanics and dynamical systems. The exposition is clear and easily understood. … This book is accompanied with a CD-ROM to complement and supplement the material in the text." (Yuan Rong, Zentralblatt MATH, Vol. 993 (18), 2002)