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During the last three years the authors of this paper have been using Mathematica to develop symbolic computing tools that, at their present stage of development, allow to: (1) calculate and topologically classify the equilibrium points of nonlinear second order dynamical systems depending on two or three parameters [2], (2) Detect and classify Poincare-Andronov-Hopf (PAH) bifurcations [5], (3) Track the dependence of flows on system's parameters through sequences of phase portraits for prescribed sequences of values of the parameters, (4) Estimate basins of attraction with Lyapunov functions [1], and (5) design linear and nonlinear controllers and observers for nth order nonlinear control systems (NLCS) [3,4,6,7]. Even though these tools were not originally developed as teaching aids, their use for such purposes might relieve students from a big amount of symbolic and graphical calculation by hand, allowing them to pay more attention to conceptual problems and to study more realistic models of physical phenomena.
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