For November 3

Section 1.5 Multiple Integrals and Approximating Sums

• To read: All
• Be sure to understand: The section Approximating Sums on page 45 and the definition of the double integral as a limit on page 47

Email Subject Line: Math 236 11/3 Your Name

Reading Questions:

1. If f(x,y) is a function of two variables, what does _R f(x,y) dA measure?
2. For any region R in the plane, what does _R 1 dA measure?

For November 5

Section 1.6 Calculating Integrals by Iteration

• To read: Through page 57. We'll talk about pages 56 and 57 in detail in class
• Be sure to understand: Examples 1 and 2

Email Subject Line: Math 236 11/5 Your Name

Reading Question:

What is the advantage of calculating double integrals by iteration?

For November 7

Section 1.6 Calculating Integrals by Iteration (cont)

• To read: Finish the section
• Be sure to understand: Example 4

No questions to email in today.

For November 10

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

Email Subject Line: Math 236 11/10 Your Name

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 November 12

Section 1.7 Double Integrals in Polar Coordinates

• To read: All
• Be sure to understand: Example 2

Email Subject Line: Math 236 11/12 Your Name

Reading Question:

Why would you ever want to convert a double integral from rectangular to polar coordinates?

For November 14

Exam 2 Today. No reading assignment.

For November 17

Section 5.1 Integrals Reviewed

• To read: All, but you can skip the section on Cylindrical and spherical coordinates. Watch out for Example 6 -- they substitute x=sin(u), which is backwards from the way we usually do a "u"-substitution.
• Be sure to understand: The statement of Theorem 1 (be warned that the notation takes some work to understand)

Email Subject Line: Math 236 11/17 Your Name

Reading Question:

The change of variables in double integrals is analagous to what technique from Calc II?

For November19

Section 5.1 Integrals Reviewed (cont)

• To read: Reread this section

No email assignment for today.

For November 21

Section 5.2 Line Integrals

• To read: All
• Be sure to understand: The definition of a line integral

Since the Takehome Exam is due today, you don't have an email assignment.

For November24

Section 5.2 Line Integrals (cont)

• To read: Reread this section and read the section Work and the Dot Product on page 105
• Be sure to understand: The section on Force and Work

Email Subject Line: Math 236 11/24 Your Name

Reading Question:

What is the physical interpretation of a line integral?

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