Math 3100
Fall 2010
Here's a link to the course syllabus.
Your first homework assignment is due Wednesday 8/25:
Section 1.1 - 3, 4, 5, 6, 8, 10,11,13
Section 1.2 - 1, 2, 6, 7
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These problems are due 9/1:
Section 1.2 - 10, 11, 13, 18, 19, 20
Section 1.3 - 2, 3, 6, 7, 8, 9
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These problems will be due on 9/8:
Section 1.3 - 11, 14, 15, 18
Section 1. 4 - 2, 3, 6, 7, 9, 10, 17
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Our first test will be on Friday 9/10 and it will cover the material covered in the above homework assignments.
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Homework for 9/15:
It only seems fair to warn you that I made the first test easier than I plan on making future tests. For homework, here are a collection of problems that would have made a slightly harder first exam.
1. Show that the limit as n approaches infinity of 1-1/n is not equal to 1/2.
2. Show that the limit as n approaches infinity of 1/(n^2-99) is equal to 0.
Also do probems (section - problem number) 1.2 - 9, 1.3 - 5, 1.4 - 11 from the book.
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Homework for 9/22
Section 1.4 - 18, 19
Section 1.5 - 1 parts a, c, e, g, i, k, m, o, 2, 3
Warning! There are lots of parts to problem 1, and we haven't gone over techniques yet in class that will do them all. Hunt through the chapter and see if you can find techniques which apply.
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Homework for 9/29
Section 1.5 - 1 parts b, d, f, h, j, l, n, 5 parts b, d, 6, 8
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Homework for 10/6
Section 1.6 - 1, 2, 3, 4, 5, 6, 7
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Our second test will be on Friday 10/8 and it will cover the material on the previous homework sets.
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Homework for 10/13
Section 1.7 - 1, 2, 3, 4, 5
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Homework for 10/20
Section 1.7 - 6, 7
Section 2.1 - 1, 2, 3, 4, 5, 7
Suppose that you inductively arrange a bunch of 2" long dominos as follows: Place the first domino on a table so that its left edge is at a point marked 0, and so the center of mass of this domino is at 1. Place the second domino underneath the first domino so that its left edge is at 1 (thus the first domino just barely balances). Keep going, this means that once the x-coordinate of the center of mass of the first n dominos is computed, you pick up the whole stack, and place it on the (n+1)rst domino so that the whole stack balances on the left edge of the bottom domino. I'd like you to find a recursive formula for the center of mass of the first n stacked dominos. What does this have to do with infinite series?
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Homework for 10/27
Section 2.1 - 8, 9, 14, 15
Section 2.2 - 1 a, c, e, g, i, k (Warning: we might not get to all techniques needed for this assignment until Monday, so be prepared to read the statement of the integral test.), 3.
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Homework for 11/3
Section 2.2 - 1 b, d, f, h, j, l, 4, 6
Section 2.3 - 1
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Homework for 11/10 (start early, there are lots of parts, but mostly they aren't too hard)
Section 2.3 - 2 b, c, 3 c, d, e, f, 5, 6, 8
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Our third test will be on Friday 11/12 and it will cover the material on the previous homework sets.
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Homework for 11/17
Section 2.4 - 1 a, c, e, g, i, k
Prop 2.26 - As you may have noticed, problem 3 on the test was a disaster. I would like you to illustrate the proof the book gives of Proposition 2.26. I want you to draw pictures of all the symbols and areas that show up in the proof. Your goal is to end up thinking that the Integral Test is easy and intuitive (and why didn't I just explain that point originally!)
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Homework for 12/3 (Friday)
Section 2.4 - 2, 4 b, 5, 6
Section 3.1- 1, 4 a, c, e
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Homework for 12/7 (Tuesday)
Section 3.2 - 1 c, d, 4 a, c, 6, 8, 11, 13
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The final exam is scheduled for Wednesday, December 15 from 12:00-3:00 in our usual room. When I wrote the course syllabus, the final was scheduled for later in the day, but the official time slot for the final is from 12-3.