Here.
Here's how grades work: add up your homework percentage, midterms, twice the final, and divide by 5.
Then find the range:
-----A
70
-----B
55
-----C
40
-----D
25
-----F
with + and - in those ranges too.
Friday, June 13, 2008
Thursday, June 12, 2008
Monday, June 09, 2008
Neeraj's office hours
"I plan on having OH on Wed 2:30-3:30 so that they can come by to pick up exams and such. (2:30 is when one finals time-slot ends, so even if students have exams that day, they can drop by between 2:30-3.)"
Office hours
I'll be in my office (7450 APM) Tuesday 11-4 and Wednesday 11-2. I'll be giving preference to my Math 109 students on Tuesday and my Ma 20b students on Wednesday, but anyone will be welcome any time.
If you want to call ahead to check "Are you already tied up with the other class?", feel free; my office number is 858-534-6450.
(Don't get 7450 and 6450 confused!)
If you want to call ahead to check "Are you already tied up with the other class?", feel free; my office number is 858-534-6450.
(Don't get 7450 and 6450 confused!)
Some practice questions (now with answers)
Of course you should look again at the practice questions for the midterms. Here are some new ones. "^" means superscript, so x^2 means x squared, etc.
1. Write out the first ten terms (up to x^9) in the Taylor series of
a) f(x) = 1 / (1-x^2)
A. We did this for 1/(1-x) and got 1 + x + x^2 + x^3 + ...
So plug in x^2, and you get
1/(1-x^2) = 1 + x^2 + x^4 + x^6 + x^8 + ... omitting terms higher than x^9.
b) (1-x^4) f(x).
A. You could take the answer above and multiply by 1-x^4. There'd be a lot of cancelation.
Or you could notice that 1 - x^4 = (1+x^2)(1-x^2), so the answer to (b) is 1 + x^2 on the nose.
2. For which values of b does
\integral_{x=0}^{infinity} (e^{bx} + e^{-bx}) dx
converge?
A. None.
If b>0, then the first term goes to infinity, and the second to zero, so the integrand doesn't go to zero (it goes to infinity).
If b<0, then the second term goes to infinity, and the first to zero, so the integrand doesn't go to zero (it goes to infinity).
If b=0, then both terms are 1, so the integrand doesn't go to zero (it's always 2).
3. You've invented the Next Big Thing. It will sell increasingly well,
until the Next Next Big Thing comes out, at which point sales will collapse.
But that won't happen until N months from now.
A representative of MicrohooTM offers you $1000 up front, plus
a pay rate of $100/month at time t. Alternately, she can offer
you a pay rate of $t/month (paid continuously), with nothing up front.
Which deal should you take? You answer should depend on N.
A. This was a lousy question (which is why I kicked it out of the final, where no question is as badly worded as this one).
What it was supposed to get across was the idea that if you take deal #1, then by time S (S < N) you've accumulated 1000 + 100*S dollars.
Whereas if you take deal #2, by time S (S < N) you've accumulated integral_{t=0}^S t dt dollars.
For S small, 1000 + 100*S > S^2/2. Whereas for S large, deal #2 is better. You can figure out when deal #2 starts to beat deal #1 by solving this quadratic equation for S. If N is less than that number, take deal #1; if N is more, take deal #2.
1. Write out the first ten terms (up to x^9) in the Taylor series of
a) f(x) = 1 / (1-x^2)
A. We did this for 1/(1-x) and got 1 + x + x^2 + x^3 + ...
So plug in x^2, and you get
1/(1-x^2) = 1 + x^2 + x^4 + x^6 + x^8 + ... omitting terms higher than x^9.
b) (1-x^4) f(x).
A. You could take the answer above and multiply by 1-x^4. There'd be a lot of cancelation.
Or you could notice that 1 - x^4 = (1+x^2)(1-x^2), so the answer to (b) is 1 + x^2 on the nose.
2. For which values of b does
\integral_{x=0}^{infinity} (e^{bx} + e^{-bx}) dx
converge?
A. None.
If b>0, then the first term goes to infinity, and the second to zero, so the integrand doesn't go to zero (it goes to infinity).
If b<0, then the second term goes to infinity, and the first to zero, so the integrand doesn't go to zero (it goes to infinity).
If b=0, then both terms are 1, so the integrand doesn't go to zero (it's always 2).
3. You've invented the Next Big Thing. It will sell increasingly well,
until the Next Next Big Thing comes out, at which point sales will collapse.
But that won't happen until N months from now.
A representative of MicrohooTM offers you $1000 up front, plus
a pay rate of $100/month at time t. Alternately, she can offer
you a pay rate of $t/month (paid continuously), with nothing up front.
Which deal should you take? You answer should depend on N.
A. This was a lousy question (which is why I kicked it out of the final, where no question is as badly worded as this one).
What it was supposed to get across was the idea that if you take deal #1, then by time S (S < N) you've accumulated 1000 + 100*S dollars.
Whereas if you take deal #2, by time S (S < N) you've accumulated integral_{t=0}^S t dt dollars.
For S small, 1000 + 100*S > S^2/2. Whereas for S large, deal #2 is better. You can figure out when deal #2 starts to beat deal #1 by solving this quadratic equation for S. If N is less than that number, take deal #1; if N is more, take deal #2.
Saturday, June 07, 2008
Sections to study for the final
5.2,3,4,5,6
6.1,2,3
7.2,6,7
9.1,2,3,5
10.1,2,3,5,7
The final will cover all of those (or, as much as can practicably be tested in 3 hours), pretty evenly. It will NOT be just stuff since the second midterm!
Same basic rules for the final -- closed book, bring one double-sided sheet of notes, no calculator, no blue book necessary -- with the extra proviso that you bring your UCSD ID. Do remember to turn off your phone... or else.
6.1,2,3
7.2,6,7
9.1,2,3,5
10.1,2,3,5,7
The final will cover all of those (or, as much as can practicably be tested in 3 hours), pretty evenly. It will NOT be just stuff since the second midterm!
Same basic rules for the final -- closed book, bring one double-sided sheet of notes, no calculator, no blue book necessary -- with the extra proviso that you bring your UCSD ID. Do remember to turn off your phone... or else.
Monday, June 02, 2008
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