Iteration is a key technique for the study of dynamical systems and is easily performed with calculators or computer software. Students no longer need to use the standard techniques of the calculus of differential equations. The improvement in visual imagery has made it easier to graphically analyze data and to display images of dynamical systems. The display may be a single snapshot or a string of pictures presented as a slide show or a short film. A variety of approaches can be taken with students at many levels.
Students can begin to analyze data and express relationships verbally.
Students will develop concepts and images for fast and slow change, increasing, decreasing, and steady-state systems. Numerical analysis can be made by finding differences, ratios, and patterns. Dynamical analysis leads to the development of discrete models based on difference equations. Advanced students can set up and analyze differential equations using numerical techniques like Euler's Method or the analytic techniques of traditional calculus classes. Some numerical techniques like Euler's Method are accessible to algebra students.