Differential Equations - Theory and Applications: With Maple

This book provides a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as important applications of the theory. The text is written to be used in the traditional way (emphasis on the theory with the computer component as optional) or in a more applied way (emphasis on the applications and the computer material). The accompanying CD contains Maple worksheets to use in working the exercises and extending the examples. The disk also contains special Maple code for performing various tasks.In addition to its use in a traditional one- or two- (there is enough material for two) semester graduate course in mathematics, the book is organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering. Researchers and professionals may also find the supplementary material on the disk on discrete dynamical systems, theory of iterated maps, and code for performing specific tasks on the disks particularly useful.

Table of Contents:
Introduction.- Techniques, Concepts & Examples.- Existence & Uniqueness-The Flow Map.- One Dimensional Systems.- Linear Systems.- Linearization & Transformation.- Stability Theory.- Integrable Systems.- Newtonian Mechanics.- Motion on a Submanifold.- Hamiltonian Systems.- Appendix A: Elementary Analysis.- Appendix B: Lipschitz Maps and Linearization.- Appendix C: Linear Algebra.

Review :
From the reviews: "This book is a comprehensive reader-friendly introduction to differential equations. a ] The theory is illustrated by a great number of nice examples, applications, figures. a ] the CD-ROM attachment is a powerful add-on resource for deeper studies and research. a ] 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 a ] the CD-ROM for improving their study, teaching and scientific work." (JAnos 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 a ] ." (J. E. Paullet, Zeitschrift fA1/4r 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 a ] . This book is accompanied with a CD-ROM for some complements and supplements. Many of thepertinent 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 a ] . the material is organized so that it can be also used in a wider setting within todaya (TM)s modern university and society. a ] The book makes every attempt to blend together the traditional theoretical material on differential equations and the new techniques afforded by computer algebra systems a ] . 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. a ] 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. a ] 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) 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." (J??nos 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 f??r 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 forsome 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)