For 1 November

• To read: Reread this section for Friday.
• Be sure to understand: Examples 3 and 6.
• Possible Reading Quiz questions:
  Decide whether the function is a solution to the differential equation.
  1. y(t)=sin(t); -y=y''
  2. y(t)=e^(2t); y=y'
  3. y(t)=(1/2)e^(t^2); y'=ty

For 4 November

For 5 November

Section 4.2 More Differential Equations: Modeling Growth

• To read: Theorem 1 on page 256, the sections on Radioactive Decay and Biological Populations on pages 259-260, and the Afterword: Discrete versus Continous Growth beginning on page 264
• Be sure to understand: The statement of Theorem 1 and Examples 3 and 4
• Possible Reading Quiz questions:
  Find a solution to each Initial Value Problem and check your answer by differentiation.
  1. y'=3y and y(0)=30
  2. y'=0.2y and y(0)=100
  3. y'=-0.01y and y(1)=12

For 8 November

• To read: Through Example 5
• Be sure to understand: The discussion on pages 297-298 begining with Local vs. Global Extreme Values and continuing through Example 3
• Possible Reading Quiz questions:
  
  1. What is the difference between a critical point of f and a stationary point of f?
  2. Where can the maximum and minimum values of continuous function occur on a closed interval?

For 11 November

• To read: All
• Be sure to understand: Examples 1, 2, and 3; The idea of marginal profit, cost, and revenue
• Possible Reading Quiz questions:
  Let P, C, and R be the total profit, cost, and revenue functions from Example 1.
  1. Give a formula for P(q) involving C(q) and R(q).
  2. When the total profit P is maximized, how are C' and R' related?
  3. In Example 1, the marginal profit at q=1500 is 0. What does this say about the graph of P?

For 13 November

• To read: Pages 326 and 327
• Be sure to understand: The statement of the Intermediate Value Theorem.
• Possible Reading Quiz questions:
  No Reading Quiz today, but you should be able to answer:
  1. What are the hypotheses of the Intermediate Value Theorem?
  2. What is the conclusion of the Intermediate Value Theorem?

For 15 November

• To read: Through page 334
• Be sure to understand: The statement of the Mean Value Theorem; the section What the MVT Says on page 333; Question 1 and Theorem 9 on page 334
• Possible Reading Quiz questions:
  Once again, no Reading Quiz today, but you should be able to answer:
  1. What are the hypotheses of the Mean Value Theorem?
  2. What is the conclusion of the Mean Value Theorem?

For 18 November

Reread these two sections and be prepared to answer the questions from the last two assignments.

For 20 November

• To read: Pages 341-349
• Be sure to understand: The definition of the integral on page 342; Example 2; the section Properties of the Integral beginning on page 345
• Possible Reading Quiz questions:
  I got this on the page a little late, so no Reading Quiz today. BUT you should be able to answer:
  1. What does the integral of a function f from x=a to x=b measure?
  2. Is the integral of f(x)=5x from x=0 to x=3 positive or negative?

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