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Exploring the phase space of a system of differential equations: different mathematical registers

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Abstract

We describe and analyze a situation involving symbolic representation and graphical visualization of the solution of a system of two linear differential equations, using a computer algebra system. Symbolic solution and graphical representation complement each other. Graphical representation helps to understand the behavior of the symbolic solution. Together with it, the symbolic solution and its analysis are needed to understand the graphical representation and to overcome the limiting constraints of the CAS. The study described in this paper points out the importance of flexibility in building connections between different mathematical registers, together with the fact that the balance between the usage of symbolic representations and of graphical representations can be very different from one student to the other.

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Correspondence to Thierry Dana-Picard.

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Research supported by Israel Science Foundation, grant number 1340/05.

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Dana-Picard, T., Kidron, I. Exploring the phase space of a system of differential equations: different mathematical registers. Int J of Sci and Math Educ 6, 695–717 (2008). https://doi.org/10.1007/s10763-007-9099-2

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  • DOI: https://doi.org/10.1007/s10763-007-9099-2

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