Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to the Hirsch, Smale and Devaney text. Unless otherwise noted, each part (a), (b), (c), etc. of a problem should be answered. You should write up solutions neatly to all problems, making sure to SHOW ALL YOUR WORK. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be YOUR OWN WORK.
Important: Please list the names of any students or faculty who you worked with on the assignment. Also be sure to cite any texts, websites, manuals, etc. you may have used.

Chapter 4 Exercises (pp. 72 - 73)
Problems:   1, 2, 3

Note: For #2, your answer should be a diagram in the ab-plane with different regions shaded according to the type of phase plane portrait (ie. saddles, sinks, spiral sinks, etc.) Label your picture carefully.

Additional Problem:
Given the following one parameter family of linear systems X' = AX, sketch the path traced out by the family in the trace-determinant plane. Describe the bifurcations that occur along this path and compute the corresponding values of a.

A =	a   a   1   0