Ordinary Differential Equations, MATH 304

Homework Assignment #1

Due Friday, September 12, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to Differential Equations, 4th ed., by Blanchard, Devaney, and Hall. Unless otherwise indicated, all parts of a problem (a), (b), etc. should be completed. You should do all of the problems; however, you only need to write up solutions for the starred (*) problems. You should also write up solutions to the additional problems based on the supplementary reading. Be sure to write up solutions neatly, making sure to show your work.

You are encouraged to work on these problems with other classmates, and it is ok to use internet sources for help if it's absolutely necessary; however, the solutions you turn in should be YOUR OWN WORK and written in YOUR OWN WORDS. Complete solutions to all problems will be posted the same day the homework assignment is due.

Important: Please list the names of any students you worked with on the assignment.

Section 1.1
Problems:   2, 4*, 5, 6, 11, 12, 17, 18*, 21, 22*

Note: Problem #11 dovetails nicely with the assigned reading on Australia (see below.)

Section 1.2
Problems:   1, 3, 8*, 9, 12, 16, 17*, 25, 26, 30, 32*, 35*, 41

Hint: You will need to use partial fractions to do the integration for #17. For #41, be sure to consider the sign (eg. + or -) for a rate of cooling.

1. Read Chapter 13, "Mining Australia," of Jared Diamond's book Collapse: How societies choose to fail or succeed.
2. Diamond mentions several examples of environmental damage, land degradation and species depletion (or growth) throughout the chapter. Pick three 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, it should contain 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?