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MATH3010.03 (Vector Integral Calculus)

# Assignments

### Assignment 7,

NOT TO BE HANDED IN

You are responsible for the material these problems are based
on however. I will give out a solution sheet on Wednesday March 29.
- Section 8.2, numbers 3, 11, 12, 25
- Section 8.4, numbers 5, 9, 10

### Assignment 6,

Due Wednesday March 29, 4:30 PM

The solution sheet will be posted outside my office as of Thursday March 30,
and will be available in class on Friday March 31.
- Section 7.3, numbers 11ab, 14
- Section 7.4, numbers 4, 7
- Section 7.5, number 7
- Section 7.6, number 9
- Page 464, numbers 22, 26
- Section 8.1, numbers 4, 9, 13

### Assignment 5,

Due Friday March 10, 4:30 PM
- Section 4.2, numbers 5, 6
- Section 4.3, numbers 2, 3, 4
- Section 7.1, number 11
- Section 7.1, number 12 or 13 (I had originally assigned 13 in class, and
12 on the web. So now you can do whichever one you want.)
- Section 7.2, numbers 2cd (do c both ways), 6, 15, 16

### Assignment 4,

Due Monday February 21, **IN CLASS**

- Section 6.2, numbers 8, 11, 13, 17, 22, 23, 26, 28, 31

### Assignment 3,

Due Friday February 4, 4:30 PM

**Postponed to Monday February 7, 4:30 PM**

Also note a small change in the second to last problem.
It should be the plane y=0, rather than x=0.
- Section 5.3, numbers 7, 13
- Section 5.4, number 2acd

**An error on the solutions sheet has been pointed out to me.
In part d, the antiderivative should be sec^5/5, not sec^6/6, making the
solution (4 sqrt 2 -1)/5.**
- Section 5.6, number 12
- Section 5.6, number 14 (evaluate it in the given order, and also rewrite
it as a triple integral in the order dx dz dy)
- Section 5.6, number 19 (rewrite it using all 6 possible orders of
the variables, and then evaluate one of these expressions)
- Let V be bounded by the surfaces x^2+z=9, z=x^2+3y^2. Express the
volume of V as a triple integral in the orders dz dy dx, and dy dz dx.
Do not evaluate.
- Find the triple integral of z over the region V bounded by the surfaces
y=0, z=0, y^2+z^2=4, x+y=2, 2y+x=6.
- Section 6.3, number 3 (read that section for the necessary definitions)

Note that I am using the notation x^2 to denote the square of x.
### Assignment 2,

Due at the beginning of class (or before class in the course mailbox)
on Monday January 24.
- Section 3.5, numbers 4, 5, 6, 8

### Assignment 1,

Due Monday January 17, by 4:30 PM

(either handed in during class, or put in the course mailbox, on the
5th floor, North wing of the Ross building, by the elevators)
- Review chapters 1 and 2 of the text.

I spent time on the material from the following sections, which I
felt were new:
- 1.5
- 2.2 (open sets - p. 94)
- 2.3 (p. 119 and 120)
- 2.5 (I'll do this Jan 10)
- 2.7 (Theorems on p. 157 and 159)

But in fact, the whole chapter should now be material you have seen
at some point, and should have some level of familiarity with.
- Section 2.3, numbers 8ac, 12ab
- Section 2.5, numbers 5a, 10, 24.

In number 5a, you should compute d(foc) three ways:
- By finding foc as a function of t and then differentiating.
- By using the coordinate expression of the text (bottom of p. 135).
- By using the matrix form of the chain rule.

- Section 2.7, number 5.