21122 Integration, Differential Equations, and Approximation
Assignments: Week #7
 Reading:
 Monday: No reading assignment in text.
 Wednesday: Section 9.5.
 Friday: Section 9.6.

 Exercises: Due Friday 13 October.
 Section 9.1 #6ac (not part b).
 Section 9.2 #12, 16, 18, 24.
 Section 9.3 #40.
 Section 9.4 #4, 10, 16, 21.
 Additional Problems: Consider the Logistic Population Model
P' = (.1) P ( 1  P/500 )
 1. Qualitative approach:
 (a) Sketch the phase line.
 (b) Using information from the phase line, sketch a representative sample
of solutions, including all constant solutions.
 (c) Sketch the solution satisfying P(0)=100.
 2. Analytic Approach:
 (a) Find an explicit formula for the solution P(t) satisfying P(0)=100. (You will
need to use an analytic method.)
 (b) Find the limit of this solution as t approaches infinity
 (c) How does this limit relate to the curves sketched in part 1(b) and (c).
 Note: Some of this weeks problems instruct you to use a "CAS". This
is an acronym for "computer algebra system," a generic way of referrint to
programs like Maple or Mathematica. For our purposes, though, the Java applet
Dfield will suit our
purposes.