We are going to extend what we learned about single DEs to systems of DEs. Our project for this part of the course will be about the interaction between interacting species, like the wolves and moose of Isle Royal. Another application will be spring-mass problems, which are also introduced in the reading for next lesson. This lesson, relate what you learned about equilibrium values and phase lines to equilibrium solutions and phase portraits. Look closely at the axes of the graphs to understand what each plot represents.
Maple does a nice job with predator-prey problems .
This lesson is on spring-mass problems. Maple can help with the visualization, but try to use mathematical reasoning to work some of the problems below before you turn on the technology. Maple can be a valuable tool, as you have seen during these lessons. Guessing is a legitimate mathematical skill, learn to develop your mathematical intuition by doing the exercises. You will do 17 and 18 in class, so you may want to look at those to prepare yourself.