The purpose of this chapter is to give an illustrated summary of some of the basic analytical and geometric ideas from ordinary differential equations (see the figures at the end of the chapter). For a more leisurely exposition of this material, you can consult sections 3.1, 4.1, and 4.4 of Braun [1983], for example, or sections 2.3, 7.1, and 9.2 of Boyce & DiPrima [1977]. You may also enjoy reading Chapter 1 of Hirsch & Smale [1974].


Phase Portrait Solution Curve Monic Oscillator Linear Harmonic Oscillator Directed Line Segment 
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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Hüseyin Koçak
    • 1
    • 2
  1. 1.Lefschetz Center for Dynamical Systems Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of Mathematics and Computer ScienceUniversity of MiamiCoral GablesUSA

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