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 9 Exercises (pp. 211 - 214)
Problems:   1a*, 1c*, 8a*, 8c*, 9b, 11

Directions: For problems #1a and #1c, first sketch the nullclines and the direction field in regions between the nullclines. Then find the equilibrium points and compute the linearization at the equilibrium points. Put all the information together to sketch the phase portrait. Feel free to use the ODE software on the webpage or MAPLE to check your sketches. For problems #8a and #8c, both systems are Hamiltonian. Give the Hamiltonian function H(x,y) and use it to help sketch the phase portrait. Again, feel free to use the ODE software on the webpage or MAPLE to aid with your sketches. Using nullclines for #8c may be helpful.