Last modified: 2010-07-13
Abstract
The study of dynamical systems requires description of mathematical relations between the variables which determine the state of the system (mathematical modeling). This is a very successful scientific research method which composes, together with the experimental work, a basis for physical theories in most cases.
In contrast to scientific research work, we often introduce simplified systems in education. Students memorize the solutions of these problems without understanding them, because they do not fit the real experiment. The problem is in differential equations, which analytical solutions are either too complex or they even do not exist.
The article shows the possibility of introducing complex dynamical systems in high school, where the role of table oriented software for numerical solving differential equations is crucial. We prepared the examples with the movement of bodies under the influence of different forces.
In these models we show the description of differential equations in the finite difference form with the help of table oriented software (Excel, Origin). Such introduction of complex systems enables the transfer of topics from everyday life to teaching, which reduces the gap between the theory and real experiment. By examining these problems students develop both natural science and digital competencies.