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Linearization and Transformation

In: Differential Equations: Theory and Applications

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  • David Betounes

    (University of Southern Mississippi, Mathematics Department)

Abstract

In this chapter we present two basic techniques that are useful for analyzing nonlinear systems. One technique consists of linearizing about the fixed points to obtain local, qualitative pictures of the phase portrait via the corresponding linear systems. Thus, our previous work on linear systems has direct bearing on nonlinear systems. The validity of this technique is contained in the Linearization Theorem, which we present later on, after first applying it in numerous examples and exercises.

Suggested Citation

  • David Betounes, 2001. "Linearization and Transformation," Springer Books, in: Differential Equations: Theory and Applications, chapter 0, pages 231-274, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-4971-7_6
    DOI: 10.1007/978-1-4757-4971-7_6
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