Write-ups due Monday April 24

Bonus problem (extra 5 points): 4b page 701 (if you have already turned it, it will be graded;
if you wish you can also turn in a (better) solution  on Apr.24)

Wednesday April 19
Solve Examples 1,2, 3 page 721.
Solve:
Sec. 20.2: 1, 3
Sec. 20.1: 1, 3,15
Sec. 20.3: Find the mass only: 1

Solve, write up and turn in:
Sec. 20.2: 2 ,5, 17
Sec. 20.1: 2, 8, 16, 18, 22
Sec. 20.3: Find the mass only: 3, 7

Thursday April 20

Solve, write up and turn in:
Sec. 20.1: 25, 27
Sec. 20.2: 7, 8, 10

Friday April 21

Topics discussed today:
a)
A.20 formulas (5),(6).; in formula (7) we wrote the absolute value of the Jacobian rather than the Jacobian itself.
We also saw the argument on page 844.
b)
Sec. 20.4 (Example 3 will be discussed on Monday.)

Solve, write up and turn in:

Sec. 20.4: 3, 12, 15, 23, 28, 31 a

Bonus problem (extra 5 points)
Explain why we do not need to use absolute value of dx/du in substitutions
in one-dimensional integrals:   dx = (dx/du) du.
Hint: use as an example, the integral between 0 and 1 of dx;
then substitute x=-2u. To make the substitution similar to the two-dimensional case,
think of your integral as an integral on the segment [0,1] (which is a region R). What is D in this example?