Mathematics 41, section 1 -- Analysis 3

Lab Day 3

February 10, 1998

The lab assignment for today is to develop solutions for parts a,c,d,e of question 1 from Discussion 12 in the Collaborative Learning Manual by Damiano and Freije. For each part you will need to:

1. Find the critical points of the given vector field F(x,y) = (u(x,y),v(x,y)) by hand, by solving the equations u(x,y) = 0 and v(x,y) = 0 simultaneously. Note: Parts d,e have several critical points. For part e, only consider the critical points in the rectangle defined by -4 < x < 4 and -4 < y < 4.
2. Plot the vector field using the fieldplot command as you did for Lab 2.
3. Plot some flow lines for the vector field. We discussed the phaseportrait command for doing this in class yesterday. The discussion uses the DEplot command, which does the same thing! Either one is OK.
4. For each critical point, determine whether it is a sink, a source, a saddle point, or a center according to our classification of critical points.

Assignment

Individual writeups due Tuesday, February 17.