Titlebook: Differential Equations: Theory and Applications; with Maple® David Betounes Textbook 20011st edition Springer Science+Business Media New Yo

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Textbook 20011st editionuld 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

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Introduction,e shall see, any higher-order system of differential equations can be reduced to a 1st-order system and thus the study of first-order systems suffices for the general theory. Many systems of differential equations model the motion of something, and for this reason systems of DEs are often referred t

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Techniques, Concepts, and Examples,pts, such as gradient vector fields, stable/unstable fixed points, separatrices, limit cycles, transformations of DEs, and conservation laws, which will be studied more formally later. Our goal is to give the reader some experience with looking at, working with, studying, and analyzing some typical

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Linear Systems,on of the flow. As would be expected, the material here relies on many topics from linear algebra and so a good background in this subject will be helpful. (Appendix C has some background material linear algebra and matrix analysis.)

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Hamiltonian Systems,hat they are related to the dynamics of motion in classical systems (through Newton’s second law). All of the previous theory and techniques apply to Hamiltonian systems, but now there are many additional features of the system, like conservation laws, a symplectic structure, and Poisson brackets, t