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The first two problems on this quiz are simply vocabulary.
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This top equation is a differential equation, as it has both functions and their derivatives mixed in
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This equation has no derivatives in it and is not a differential equation
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Differential equations are used to model flows
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The second equation is a difference equation
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Difference equations are used to describe or model maps
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Question 3 asks us to characterize each of these four fixed points as stable, unstable, or chaotic
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As it makes no sense to have a chaotic fixed point, we can eliminate this choice from all of the questions
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To analyze whether these fixed points are stable or unstable, we need to know whether a small perturbation near the fixed point grows or shrinks
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For this first fixed point, notice that a small perturbation quickly shrinks down and the pendulum returns to the original fixed point
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So this fixed point is stable. That is the answer to 3a
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For this fixed point in figure 1b, notice that the small perturbation caused by my finger rapidly grows
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That means this fixed point is unstable. That is the answer to 3b
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Notice for c and d, I have to hold them in position
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That is, they are so unstable, I cant even get them to balance at this point
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That should give you a hint as to the answer for these problems
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But to make it very clear, watch small perturbations of both c and d
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As you can see, both c and d are also unstable fixed points. That is the answer to 3c and 3d