Math 2934 homework
1. (due 8/26) Be sure you know how to do any of 13.1 # 1-18 (but ignore #9, as we will
have much better ways to do that later on). Hand in 13.1 # 4, 10, 12, 17. Also be
able to do any of 13.1 # 23-30, no need to hand any in. Also hand i
Mathematics 2934-010
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Quiz 6
December 1, 2011
Instructions: Give concise answers, but clearly indicate your reasoning. Remember that
mean the gradient of f .
I.
(2)
State Greens Theorem for a domain D with boundary a positively oriented
Mathematics 2934-010
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Quiz 6
December 1, 2011
Instructions: Give concise answers, but clearly indicate your reasoning. Remember that
mean the gradient of f .
f and grad(f ) both
I.
(2)
State Greens Theorem for a domain D with boundary a
Mathematics 2934-010
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Quiz 5
November 3, 2011
Instructions: Give concise answers, but clearly indicate your reasoning.
I.
Consider the solid in the rst octant bounded by the three coordinate planes and the plane 3x + 2y + z = 6.
(6)
(a)
Math 2934 homework
35. (12/2) 17.4 # 1, 5, 8, 11, 14, 22, 23, 27 (also tell why Greens Theorem does not show
it must be zero for loops that do enclose the origin)
36. (12/2) 17.5 # 12
37. (12/2) As many as needed from 17.5 # 1-8, 13-18. Look at 17.5 # 23-
Mathematics 2934-010
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Quiz 4
October 6, 2011
Instructions: Give concise answers, but clearly indicate your reasoning.
Remember that
d
1
arctan(x) =
.
dx
1 + x2
I.
Calculate the following partial derivatives.
(7)
1
1. ft (x, y, z, t) if
Mathematics 2934-010
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Exam II
October 17, 2011
Instructions: Give concise answers, but clearly indicate your reasoning. Do not simplify the answers unless you
nd yourself with enough time at the end.
I.
(12)
Calculate the following.
1.
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Quiz 3
September 29, 2011
Instructions: Give concise answers, but clearly indicate your reasoning.
I.
(15)
For the vector-valued function r(t) = cos(t2 ) + sin(t2 ), the velocity is v(t) = 2t sin(t2 ) + 2t cos(t2 )
Mathematics 2934-010
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Quiz 2
September 8, 2011
Instructions: Give concise answers, but clearly indicate your reasoning.
I.
(3)
Find the cosine of the angle (you dont need to nd the angle itself) between the diagonal of a cube and
one of
Mathematics 2934-010
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Exam I
September 19, 2011
Instructions: Give concise answers, but clearly indicate your reasoning. Do not simplify the answers unless you
nd yourself with enough time at the end.
I.
Let L be the line through the po
Math 2934 homework
43. As many as needed from 17.9 # 1-14, including at least 1, 3, 11, 13. Also look at 19,
24 (notice that 2x + 2y + z 2 = (2 + 2 + z k) (x + y + z k) and (x + y + z k) is
2x + 2y + z 2 dS
the unit outward normal of x2 + y 2 + z 2 = 1, s
Mathematics 2934-010
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Quiz 1
August 30, 2011
Instructions: Give concise answers, but clearly indicate your reasoning.
I.
(4)
Draw a sketch of the sphere that that passes through the origin and has center (1, 1, 2). Write an equation
for
Math 2934 homework
26. (11/4) Suppose you have a function g(u, v) of two variables. Its domain is a region R
in the uv-plane. Consider its graph in uvw-space, w = g(u, v).
(a) For a small rectangle of sides ui and vj in the uv-plane, whose lower left corn
Math 2934 homework
11. (9/26) As many of 9-26 as needed. Hand in 14.2 # 5, 7 (note that y = x3 ), 12 (sin1 t
means the inverse sine function from Section 7.6, now would be a good time to review
them), 13, 15-16, 20, 26.
12. (9/26) 14.2 # 34, 36. 14.3 # 3
Mathematics 2934-010
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Quiz 5
November 3, 2011
Instructions: Give concise answers, but clearly indicate your reasoning.
I.
Consider the solid in the rst octant bounded by the three coordinate planes and the plane 3x + 2y + z = 6.
(6)
(a)