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 deemphasize
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 :
 Why would you ever want to convert a double integral from rectangular to polar coordinates?
 What is the shape of a polar rectangle?
For April 10
Section 3.3 Double Integrals in Polar Coordinates
Reread 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 :
 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.
 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 :
 What are the domain and range of the functions f and gamma involved in a line integral?
 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 g_{1} be the parametrization g_{1}(t)=(t, 2t) for 0<=T<=2
and g_{2} be the parametrization g_{2}(t)=(2t, 4t) for 0<=T<=1.
How are
_{g1}f(X) dX and
_{g2}f(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:
 What is a potential function ?
 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:
 What are the two types of functions involved in Green's Theorem? Is this surprising?
 In nontechnical 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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