21-117: Integration and Differential Equations

Exam #2: Review

• The Exam covers Sections 8.1, 9.1-9.5 and 17.1.

• Review Problems:
  Section 8.1: #9, 17, 21, 35.
  Section 9.1: #5, 6, 12.
  Section 9.2: #2, 7, 11.
  Section 9.3: #3, 10, 13, 31, 37, 38.
  Section 9.4: #1, 5, 13, 15.
  Section 9.5: #14. (draw the phase line for this system).
  Section 17.1: #11, 13, 21.
  Section 17.3: #2, 3, 5, 6.

  Additional Problems

  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 amount 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 spread 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?