Math 236 - Multivariable Calculus
Reading Assignments - April 2003

Be sure to check back, because this may change during the semester.
(Last modified: Wednesday, January 15, 2003, 10:12 AM )

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

For April 2

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 4

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 7

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 9

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

For April 11

Exam 2 today. No reading assignment.

For April 14

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 (-2,2), 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 16

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

Reading Question :

    What are the domain and range of the functions f and gamma involved in a line integral?

For April 18

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 :

    If g1 and g2 are different parametrizations of the same path, how are the line integrals g1f(X) dX and g2f(X) dX related?

For April 21

Section 5.2 More on Line Integrals; a Fundamental Theorem
Reread the section and be sure to understand the statement of Theorem 2, the Fact on page 262, but there are no Reading Questions for today.

For April 23

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 25

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.

For April 28, 30, and May 2

Course overview and the REALLY big picture. No reading assignments.
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Last modified: Wednesday, January 15, 2003, 10:12 AM