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 1 Exercises (pp. 16 - 19)
Problems:   10, 13, 15, 16

Hints and notes: For problem #10b, you should first prove that your general solution from #10a contains all possible solutions. This can be done in a manner similar to the argument given in class for x' = ax (Section 1.1). For problem #15, what can you say about the Poincare map? You may assume that the Poincare map is continuous. (In fact, it is actually differentiable and increasing, as shown in Section 1.5.)