Math 236 - Multivariable Calculus Reading Assignments - April 2002

Be sure to check back, because this may change during the semester.

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

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

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
• Be sure to understand : The section "Polar Integration - How It Works"

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

For April 12

Exam 2 today. No reading assignment.

For April 15

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

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

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
• Be sure to understand : The statements of Theorem 1 and 2, and Example 4.

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
• Be sure to understand : The statement of Theorem 2

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.

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