Titlebook: Ordinary Differential Equations: Basics and Beyond; David G. Schaeffer,John W. Cain Textbook 2016 Springer Science+Business Media New York

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David G. Schaeffer,John W. Cainw only been available scattered in journals and conference pInformation is precious. It reduces our uncertainty in making decisions. Knowledge about the outcome of an uncertain event gives the possessor an advantage. It changes the course of lives, nations, and history itself. Information is the foo

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Linear Systems with Constant Coefficients,n, we shall let . be the dimension of our systems, so that the index . is available for other uses.) The written-out system (.) is awkward to read or write, and we shall normally use the vastly more compact linear-algebra notation . where . = (.., .., ., ..) is a .-dimensional vector of unknown func

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Nonlinear Systems: Local Theory, for systems of nonlinear ODEs. For the moment we consider only autonomous systems, say . where .; or more generally, we may assume that . is defined only on an open subset .. In Section ., we discuss extensions of the theory to nonautonomous systems.

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Oscillations in ODEs,representative of the kind of behavior we focus on. Up to now, we have been forced to rely on the computer to study such phenomena. In this chapter, we introduce analytical techniques to predict and describe oscillatory behavior.

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