Linear Systems in the Plane

  • Stephen Lynch


  • To introduce the theory of planar autonomous linear differential equations.

On completion of this chapter, the reader should be able to
  • classify critical points in the plane;

  • carry out simple linear transformations;

  • construct phase plane diagrams using isoclines, direction fields, and eigen-vectors.


Vector Field Phase Portrait Unstable Manifold Stable Manifold Solution Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Recommended Textbooks

  1. [1]
    J. Cronin, Differential Equations: Introduction and Qualitative Theory, Second ed., Marcel Dekker, New York, 1994.MATHGoogle Scholar
  2. [2]
    D. K. Arrowsmith and C. M. Place, Dynamical Systems, Chapman and Hall, London, 1992.MATHCrossRefGoogle Scholar
  3. [3]
    D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, Second ed., Oxford University Press, Oxford UK, 1990.Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Stephen Lynch
    • 1
  1. 1.Department of Computing and MathematicsManchester Metropolitan UniversityManchesterUK

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