For April 2

• To read: Reread this section for Friday.
• Be sure to understand: Examples 3 and 6.
• Reading 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 April 4

• 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
• Reading Questions:
  Because of the Differentiation Exam, you don't need to send these in, but you think about the problem:
  Find a solution to the Initial Value Problem y'=3y and y(0)=30 and check your answer by differentiation.

For April 7

• To read: All, but you may skip the section on Root-Grubbing for Money: IRAs and Newton's Method.
• Be sure to understand: The basic idea of Newton's Method; Example 5
• Reading Questions:
  
  1. What is the purpose of Newton's Method?
  2. Explain in a couple of sentences the idea behind Newton's Method.

ForApril 9

• 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
• Reading 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 April 11

For April 14

• To read: All
• Be sure to understand: The statement of the Intermediate Value Theorem, Example 2
• Reading Questions:
  
  1. What are the hypotheses of the Intermediate Value Theorem?
  2. What is the conclusion of the Intermediate Value Theorem?

For April 16

• 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
• Reading Questions:
  
  1. What are the hypotheses of the Mean Value Theorem?
  2. What is the conclusion of the Mean Value Theorem?
  3. Explain the MVT using "car talk" (that is, using velocity).

For April 18

For April 21

• 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
• Reading Questions:
  
  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?

For April 23

• To read: All
• Be sure to understand: The definition of the Area Function on page 357; Examples 1 and 2
• Reading Questions:
  
  1. Let f be any function. What does the area function A_f(x) measure?
  2. Let f(t)=t and let a=0. What is A_f(1)?

For April 25

For April 28

• To read: All, except that you may skip the proof of the FTC beginning on page 373 (we'll see a different proof in class)
• Be sure to understand: The statement of both the first and second forms of the Fundamental Theorem; Example 3
• Reading Questions:
  
  1. Find the area between the x-axis and the graph of f(x)=x^3 + 4 from x=0 to x=3.
  2. Does every continuous function have an antiderivative? Why or why not?
  3. What is the difference between a definite integral and an indefinite integral?

For April 30

• To read: Through page 382
• Be sure to understand: The figures on page 378; the section on Sigma Notation beginning on page 380
• Reading Questions:
  Let f(x)=x^2 and let I represent the integral of f from x=0 to x=3.
  1. Estimate I by finding L_3, the left sum with 3 equal subintervals.
  2. Estimate I by finding R_3, the right sum with 3 equal subintervals.

For May 2

• To read: Finish reading the section.
• Be sure to understand: The definition of a Riemann sum on page 383.
• Reading Questions:
  Nothing to send in today, but think about:
  • Why does the limit definition of the integral on page 383 make sense?
  This takes some work to understand.

Back to the Math 101 Page