Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to Differential Equations, 3rd ed., by Blanchard, Devaney, and Hall, the required text for the course. 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 you worked with on the assignment.

Section 1.1
Problems:   3, 4, 6, 11, 12, 15, 18, 19, 20, 21

Note: Problem #6 dovetails nicely with the assigned reading on Australia (see below.)

Section 1.2
Problems:   1, 3, 8, 11, 15, 18, 25, 27, 28, 33, 35

Hint: You will need to use partial fractions to do the integration for #15. For #35, be sure to consider the sign (eg. + or -) for a rate of cooling.

Additional Problems:

1. Read Chapter 13, "Mining Australia," of Jared Diamond's book Collapse: How societies choose to fail or succeed (class handout).
2. Diamond mentions several examples of environmental damage, land degradation and species depletion (or growth) throughout the chapter. Pick four of these examples and model them using a differential equation. Indicate what your variables represent, the type of population model you chose and why, based on the reading. At least one of your examples should be a system, that is, containing more than one dependent variable. To get started, refer to the examples in the text and in the homework exercises for Section 1.1.
3. Although Diamond provides an overwhelming amount of disconcerting evidence for the future of Australia, he ends the chapter with some "signs of hope." Take two of your models from the previous question and adjust them to reflect some of these signs of hope. Be specific, backing up your conclusions with facts from the reading.
4. Based on your reading, what do you expect the population of Australia to be in 50 years?