One of the main ideas in the reading was that, even in a diff eq can be solved algebraically, sometimes it is better to analyze it graphically. The technique that comes out of this idea is interpreting a diff eq's as vector fields. If you plot the diff eq on a graph and then put arrows along the x axis representing the velocity (arrow points to the right if velocity if positive; to the left if it's negative), it becomes easy to see what happens from different initial conditions as t approaches infinity.
Challenges:
In 2.2.2 and 2.3 I didn't quite follow how the author plotted the graphs from equations with several variables. Perhaps I need to review my physics equations and perhaps it's not crucial that I know how he derived the graph but he seemed to jump straight from the equation to the graph, and I got lost.
Reflections:
Overall in this reading I liked how the techniques made complicated problems simple. Specifically, in example 2.2.3 instead of trying to graph f(x)=x-cosx, the author simply broke it into 2 seperate, easily-graphable parts, and analyzed it from there. I'm used to doing ugly problems the hard way, so this chapter looks like a nice alternative.
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