21-117: Integration and Differential Equations

Homework

• There is no homework due on Tuesday, February 29. You should begin reviewing for your Second Exam on Friday, March 3.

Homework #11

• Due at the start of Recitation on Thursday, March 1.

  Read:

  Section 9.4
  Class Notes from Wednesday, February 23.
  Section 17.1

  Exercises:

  Section 9.4: #10, 12, 13.

  Lecture, February 23:

  1. Consider the logistic growth model, modified for a constant rate of hunting: dP/dt = .1 P ( 1 - P/1000 ) - h. If h=10, what long term predictions does the model make? What is the minimum population that can sustain this ammoint of hunting?
  2. Using the same model with h=30, what predictions can you make?
  3. The logistic model dP/dt = .1 P ( 1 - P/1000 ) can be modified to include the effect of disease on the population. The rate of sspread of disease is proportional to the square of the population size. So we should consider the model dP/dt = .1 P ( 1 - P/1000 ) - dP^2. How does the carrying capacity depend on the constant d? What is the carrying capacity if d=.01?

  Section 17.1: #5, 10, 17.