Assignment For Section 2.1 & 2.2

You should read the section before attempting any reading questions or problems. Remember that you are responsible for all definitions and examples. Also remember to keep the answers to the reading questions on a separate piece of paper; these will be randomly collected from time to time.

1)    Define in your own words each of the following terms. Include examples to clarify your definitions.
a)    limiting population (*)                           c)    threshold population
b)    carrying capacity    (*)                           d)    stable critical point

(*)    Note that the limiting population and the carrying capacity are not the same. To see this consider harvesting example 4 on page 92 with k=1, M=4, and h=3. The harvesting does lower the limiting population from 4 to 3, but does harvesting affect how much the environment can hold?

2)     On page 77, what method did the authors use to integrate ?
(Do not integrate; just explain the method.)

3)    Use substitution to verify that Eq (4) is a solution of Eq (3) on page 77.

4)    What is the relationship between critical points and equilibrium solutions. Recall that an equilibrium solution is one in which the y-values stay constant as the x-values change (ie y(x)=constant).

Problems:
page   84     2, 5, 7  , 9, 11, 14, 15, 19, 21, 22, 25, 27
page   93     2, 5, 12, 14, 18, 20