21-122 Integration, Differential Equations, and Approximation
Assignments: Week #7
- 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