Differential equations as a teaching topic in school?

Autores: Karl Heinz Keunecke
Localización: Boletín de la Sociedad Puig Adam de profesores de matemáticas, ISSN 1135-0261, Nº. 54, 2000, págs. 18-28
Idioma: inglés
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Resumen
- Some pocket calculators comprise a computer algebra system (CAS). These new tools force educators to reassess the mathematics curriculum since they allow to teach new topics in math and science. Will the CAS bring differential equations and the pertaining solution methods to school? This article presents some ideas about how to introduce differential equations in math or physics. At first a numerical method for solving first and second order differential equations ought to be explained to the students. Then they have to learn how the results can be presented on pocket calculators such as Tl-89 and TI-92 Plus making use of tables and the different graphical displays. The numerical solvers of these pocket calculators are then applied to the differential equations of linear and nonlinear oscillations. The simulation of the oscillations of a physical pendulum at large angular displacements are compared with observations. It is further shown that even chaotic oscillations can be modeled and the typical features of such motions like chaotic transitions, bifurcations, sensitivity with respect to initial conditions etc. can be demonstrated.