| HW
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Assignments (due in class, no late HW accepted)
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| HW #1 (due 3/15)
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READ 6.3, 7.2
DO 6.3 ( 8, 12, 13, 15, 19 )
AND 6.1 ( 7 ) by "closing the path" and using Green's theorem
AND 6.4 ( 20 ) <-- careful, F is not conservative!
AND 6.4 ( 22 ) <-- hint: d/dt[ x(t) DOT y(t) ]=x'(t)y(t)+x(t)y'(t)
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| Mon 3/25
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no HW due; welcome back from break!
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| HW #2 (due Wed 3/27)
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READ 7.1-7.2 (and REVIEW 1.7 if needed)
DO 1.7 ( 23, 25, 27, 33 )
Problem A. Calculate the lateral surface area of a cylinder
of radius A and height H, using an appropriate
surface integral.
7.2 ( 5 ) <-- do each side of the cube separately, then add!
7.2 ( 6 ) <-- use method discussed in class
7.2 ( 7 ) <-- for part (b), think about what the surface
integral means!
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| HW #3 (due Mon 4/1)
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READ 7.1-7.3
DO 7.1 ( 1, 11, 19, 22 )
AND 7.2 ( 1, 2, 9, 11, 13, 15 )
<-- p.s. a "closed" cylinder is capped off
by top and bottom discs. You should parametrize each of the
surfaces involved. Try polar coordinates for the flat top and bottom.
Hint: symmetry may help with the calculations.
SHOW ALL WORK.
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| HW #4 (due Wed 4/3)
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READ 7.3
DO 7.1 ( 7 ) 7.2 ( 17, 20 ) 7.3 ( 1, 2, 4 )
Hint: calculations may simplify if you think about
the geometry of what is going on.
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| HW #5 (due Fri 4/5)
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READ 7.3 again
DO 7.3 ( 5, 6, 9, 11 ) and Problem A assigned in class on 4/3.
Check the date
to make sure you are doing the right HW!
Don't forget that I have office hours
on Tue, Thu from 4-5pm, and that the course tutor is available
for help Sun, Tue, Thu nights at 10:30pm!
See info at top of page.
Your first exam is coming up next week,
handed out Wednesday in class, to be turned in Friday.
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| HW #6 (due Mon 4/8)
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READ 7.4 and REVIEW for your EXAM!
DO 7.3 ( 10, 14, 26 ) 7.5 ( 7, 16, 22 ) 6.2 ( 5a ) 6.3 ( 17 ) 6.4 ( 1a )
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| no HW (Wed 4/10)
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REVIEW for your EXAM, pick up EXAM in CLASS. No exceptions.
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| Fri 4/12
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HAND IN YOUR EXAM in class.
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| HW #7 (due Mon 4/15)
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READ 4.1, 4.2
DO 4.1 ( 6, 7, 8, 9, 10 ) 4.2 ( 3, 5, 8 )
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| HW #8 (due Wed 4/17)
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READ 4.3
DO 4.1 ( 14, 15, 19ab ) 4.2 ( 7, 12, 17, 20, 23b, 28, 29 )
<--- on problem 29, it is easier (and equivalent) to minimize the
square of the distance
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| HW #9 (due Fri 4/19)
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READ 4.3
DO 4.2 ( 21, 22, 30, 32, 33 )
<--- on problem 30, to optimize the function on the boundary, you
need to check the 4 sides and 4 corners.
on problem 32, it may be easier to parametrize the
boundary by cos(t), sin(t), then optimize in t.
[p.s. don't use Lagrange multipliers for these, since we haven't
talked about them yet.]
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| HW #10 (due Mon 4/22)
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READ 4.3
DO 4.3 ( 1, 2, 3, 5, 6, 18, 19, 20 )
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| HW #11 (due Wed 4/24)
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READ 4.4
DO 4.3 ( 21, 25, 27, 29 ) 4.4 ( 13 )
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| Fri 4/26
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NO CLASS this FRIDAY. See HW for Monday below.
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| HW #12 (due Mon 4/29)
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Check the date; make sure you are doing the
correct assignment.
READ 3.1-3.2 [focus on Kepler's laws and Frenet frames]
DO 3.1 ( 4, 10, 15, 25, 26 ) 3.2 ( 12 )
<---- on the last problem, use equation (4) on p.200.
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| HW #13 (due Wed 5/1)
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READ 3.2, especially Examples 5-10.
3.2 ( 13, 14, 17 )
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