Math 236 - Multivariable Calculus
Reading Assignments - April 2002

Be sure to check back, because this may change during the semester.
(Last modified: Friday, March 29, 2002, 9:55 AM )

I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Multivariable Calculus by Ostebee/Zorn.

For April 1

Section 3.2 Calculating Integrals by Iteration
Reread the section, especially the proof of Theorem 1 but there are no reading questions for today.

For April 3

Appendix B Calculus in Polar Coordinates
  • To read : All, but you can de-emphasize the part before the section on Finding Area in Polar Coordinates
  • Be sure to understand : The section Finding Area in Polar Coordinates

Reading Question :

    When approximating an area in rectangular coordinates, we form rectangles each of width x. In polar coordinates, what do we form rather than rectangles?

For April 5

Appendix B Calculus in Polar Coordinates
  • To read : Reread the section on Finding Area in Polar Coordinates

Reading Question :

    Set up the integral that gives the area of one leaf of the polar rose r = sin(3 theta).

For April 8

Section 3.3 Double Integrals in Polar Coordinates
  • To read : All
  • Be sure to understand : The section "Polar Integration - How It Works"

Reading Questions :

  1. Why would you ever want to convert a double integral from rectangular to polar coordinates?
  2. What is the shape of a polar rectangle?

For April 10

Section 3.3 Double Integrals in Polar Coordinates
    Re-read the section, but no reading questions for today.

For April 12

Exam 2 today. No reading assignment.

For April 15

Section 5.1 Line Integrals
  • To read : All
  • Be sure to understand : The definitions of a vector field and of the line integral

Reading Questions :

  1. Consider the vector field graphed in Example 2. If you dropped a particle at the point (-2,4), describe the path that the particle would follow.
  2. Consider the vector field graphed in Example 1. If you dropped a particle at the point (2,2), describe the path the particle would follow.

For April 17

Section 5.1 Line Integrals
  • To read : Reread the section for today.

Reading Question :

  1. What are the domain and range of the functions f and gamma involved in a line integral?
  2. What physical quantity does a line integral measure?

For April 19

Section 5.2 More on Line Integrals; A Fundamental Theorem
  • To read : All
  • Be sure to understand : The statements of Theorem 1 and 2, and Example 4.

Reading Question :

    Let g1 be the parametrization g1(t)=(t, 2t) for 0<=T<=2 and g2 be the parametrization g2(t)=(2t, 4t) for 0<=T<=1.
    How are g1f(X) dX and g2f(X) dX related?

For April 22

Section 5.2 More on Line Integrals; a Fundamental Theorem
  • To read : All
  • Be sure to understand : The statement of Theorem 2

Reading Questions:

  1. What is a potential function ?
  2. What is the advantage of potential functions when calculating line integrals?

For April 24

Section 5.3 Relating Line and Area Integrals: Green's Theorem
  • To read : Through page 271
  • Be sure to understand : The statement of Green's Theorem. This is a hard section. We'll talk about the proof in class.

Reading Questions:

  1. What are the two types of functions involved in Green's Theorem? Is this surprising?
  2. In non-technical terms, what is special about the curve in Green's Theorem?

For April 26

Section 5.3 Relating Line and Area Integrals: Green's Theorem
  • To read : Reread through page 271
  • Be sure to understand : All the conditions of Green's Theorem

Reading Question:

    Give an example of a region R in the plane where Green's Theorem does not apply.
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Last modified: Friday, March 29, 2002, 9:55 AM