Describe in your own words
Euler's Method for approximating the solution of a first-order initial
value problem.
Why do you think Euler's
Method failed to produce a good approximation when the number of steps
was too small? Why did you get the particular approximation you saw
at the end of Part 2?
Why does the solution of
dy/dt = sin(y),
with y(0) = 0.1.
look similar to the solution of
dy/dt = y (1 - y),
with y(0) = 0.1?
Describe all equilibrium solutions of the Logistic Equation.
In what ways are the solutions of the Logistic Equation and of dy/dt
= sin(y) similar? In what ways are they different? [Ignore numerical differences
and concentrate on differences of shape.]
