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ERIC Number: EJ884056
Record Type: Journal
Publication Date: 2010
Pages: 7
Abstractor: As Provided
Reference Count: 8
ISBN: N/A
ISSN: ISSN-0020-739X
Separatrices
Fay, Temple H.; Joubert, Stephan V.
International Journal of Mathematical Education in Science and Technology, v41 n3 p412-418 2010
In this article we examine 2 x 2 first-order systems of ordinary differential equations and show how to identify separatrices for phase plane portraits when the system has a saddle point critical value. We describe how to use a computer algebra system to generate trajectories from contour plots, when possible, and determine the equation of the separatrix. When this approach is not possible, we describe how to use numerical investigations to determine the separatrix. Generating a phase plane portrait is useful, for at a glance one can observe what initial values give rise to bounded solutions, periodic solutions and other important features. It also permits the instructor to concentrate on the qualitative aspects of the model under investigation rather than the calculational difficulties associated with finding solutions. A list of examples suitable for student study is given in an appendix. (Contains 3 figures.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A