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**