### Homework assigned 12/1, due 12/8

### My office hours on Monday 12/7 will be 6-7, rather than 4-5.

### Section 8.8

Problems 4 - 8

For problem #4, you'll need to modify the two codes from the web-page
so that you have the right stopping criterion. Make sure to hand in
copies of your modified code.

For problem #7, use the zero vector as your first guess.

### Section 9.1

Problems 2b, 3b, 6

For the following problem, assume that y(x) is a real-valued
function.

A) For y' = a y, find all the fixed points of the ODE. Find whether
points initially near the fixed points move toward the fixed point
or away from the fixed points. How does your answer depend on the
constant a?

B) For y' = y^2, find all the fixed points of the ODE. Find whether
points initially near the fixed points move toward the fixed point
or away from the fixed points.

C) For y' = -y^2, find all the fixed points of the ODE. Find whether
points initially near the fixed points move toward the fixed point
or away from the fixed points.

D) For y' = y^3, find all the fixed points of the ODE. Find whether
points initially near the fixed points move toward the fixed point
or away from the fixed points.

E) For y' = -y^3, find all the fixed points of the ODE. Find whether
points initially near the fixed points move toward the fixed point
or away from the fixed points.

F) For y' = a + y^2, find all the fixed points of the ODE. Find whether
points initially near the fixed points move toward the fixed point
or away from the fixed points. How does your answer depend on the
constant a?