Mathematics 2210 Homework
Calculus III, Section 1, Fall Semester, 2014
Feel free to see me if you want your homework problems glanced over. Explain your work as
necessary! Explanations, organization, and neatness all matter.
Some Preliminary Practice with Vectors (optional)
Set 0: 11.2 13 - 16, 20, 24, 35
Homework set 1: Due Friday, 9/12
Notes:
11.5: #34 - you may leave this as a definite integral, if you wish
11.7: #30 - don’t bother with the binormal vector. Start by TRYING to find r’ at t1
11.7: #36 - annoying; extra credit
Set 1: 11.3
2,4, 6, 12, 16, 26, 70, 74
11.4
1, 2, 12, 14, 34 (why?), 35
11.5 6, 8, 22, 26, 34, 36, 40, 45a (explain)
11.6
2, 6, 8, 14, 21, 32
11.7
8, 10, 30, 36, 86
Homework set 2: Due Monday, 9/22
Notes:
11.8 # You don’t have to name the graph - but show some slices of the surface to justify your
final graph
12.2 # The cosh function is defined as cosh(ct) = 21 (e−ct + ect )
Set 2:
11.8
12.1
12.2
12.3
8, 16
18, 20, 22
34, 46
12, 14
Homework set 3: Due Friday, 10/03
Notes:
12.5 Don’t forget to normalize the direction vector in your answer (its length should be 1)
12.6 Volume of a cone of radius r, height h is V = πr2 h3
Set 3: 12.4
4, 6, 9, 10
12.5
2, 4, 5, 16, 26
12.6
3, 4, 6, 7, 8, 10, 20
12.7
5, 6, 7
1
Homework set 4: Due Monday, 10/20
Notes: I’ve added a few more problems from 12.7
Set 4: 12.7
18, 21, 23
12.8 2, 7, 11, 30, 36
12.9
3, 5, 10, 27
Homework set 5: Due Friday, 10/31
Notes:
Set 5:
13.1
13.2
13.3
13.4
11
3, 9, 16, 24
16, 17, 18, 39
7, 21, 24, 35, 39
Homework set 6: Due Monday, 11/10
Notes: On problem 13, just find the mass and center of mass of the object
13.6: #10 - use the integration formula 16 in the back of the book - leave this in cartesian coordinates!
Set 6: 13.5 3, 13, CM (see below)
13.6
7, 10, 15, 18
13.7
23, 24, 33 (a and b)
13.8
8, 11, 16, 20
CM: Find the center of mass of the region between y = 0 and y = e−x , and x = 0 and x = ∞.
Assume the density of the object is a constant (δ(x, y) = k).
1. Sketch a graph of the region
2. Calculate the mass, x̄, and ȳ for the truncated region between y = 0 and y = e−x , x = 0 and
x = b.
3. Take the limit as b → ∞
Homework set 7: Due Wednesday, 11/26
Notes:
13.9 #17 requires integration formula 66 from the back of the book
13.9 #18 Just rewrite this integral in terms of the transformed coordinates
Set 7:
13.9
14.1
14.2
2, 4, 17 - 19
14, 15, 18, 25
7, 15, 19, 21 25
2
Homework set 8: Due Wednesday, 12/10
Notes: Changed my mind - this is the complete homework set.
Set 8: 14.3
3, 6, 11, 13, 20, 22, 24
14.4 3, 4, 5, 10, 12, 14, 15, 19
Homework set 9:
Notes: These problems are all optional (I will not collect/grade this assignment).
14.6: Be able to set up any of these problems as surface integrals
14.7: I’ll add a couple from 14.7 as well on Friday
Set 9: 14.5 7, 9, 11, 13, 29a
14.6
4, 5, 13, 15
14.7
3