Math 2B Discussion Sections 80 & 81 (Fall 2004)
2^nd Quarter Calculus

Cute Integration Tricks
Posted Dec. 2, 2004, 1:42pm

Today in class, we came up wtih an alternative method to integrate sec θ and csc θ. I cleaned up our work and put it into a PDF file. I'll try to get some examples on integration by partial fractions up in the next couple of days. For now, see below to get this download.

I just noticed a typo!
Posted Dec. 2, 2004, 9:47am

I just noticed a typo on my handout for the trig integrals. You should use the following substitutions:

Handout for Trig Integrals (Update)
Posted Nov. 25, 2004, 1:30pm

I updated the last example to complete the exercise. Upon request, I can add a few more there.

Handout for Trig Integrals
Posted Nov. 25, 2004, 3:59am

I wrote up a handout with some integration examples using some of the various techniques for integrals involving trig functions. Please see the handout posted below.

I am an idiot.
Posted Nov. 23, 2004, 10:00am

Dear Class,

First and foremost, please let me apologize for my mistake this morning. I was working on the midterm 2 solution guide, and for some reason I completely forgot that class is at 9:00am, rather than 9:30am. I am terribly sorry for the any inconvenience caused by this. I don't think I've ever made a blunder like this before.

Anybody enrolled in my 9:00am class is entitled to an office hour anytime today or tomorrow from 7am to 5pm, except at the following times:

Today (Tuesday): 3:30 pm - 5:00 pm
Tomorrow (Wednesday): 11:00 am - 12:00 noon

Please email me if you would like to make such an appointment.

Also, though it came at a terrible cost, the midterm 2 solutions are up. Please have a look at this link.

(If you can't read the entire link, just start at this link, and browse to the bottom of the page.)

Lastly, please note that course evaluations will be handed out next Tuesday.

Once again, I'm very sorry for any inconvenience caused by my absent-mindedness. I hope you all have a fantastic Thanksgiving holiday!

Sincerely,

Paul Macklin
TA for Math 2B, Sections 80 and 81
Department of Mathematics
UC-Irvine

Midterm 2 Solution Guide
Posted Nov. 23, 2004

I'm sorry that it took me so long to get this written up! The link is at the bottom of the page.

Midterm 2 Results and Statistics
Posted Nov. 18, 2004:

Barring any changes in plans, I'm planning upon returning them today. If you are in Tuesday's section, you can come before or after class today (11:00-11:50 in IERF B015), in office hours today from 9:30-11:00, or next Tuesday during class or office hours.

Some basic statistics:

low score: 6
high score: 100
average: 68.58
standard deviation: 21.58

Here's what the distribution of grades looked like:

Overall, performance was okay, but I do have a few comments:

1) Those who were less organized tended to make more mistakes. Furthermore, those who failed to show their work were unable to receive much partial credit when things went wrong. Lastly, when answers magically appeared without any supporting work on a nontrivial problem, I awarded little-to-no credit.

2) Some people need to be very careful in distinguishing between differentiation and integration. I saw people with scratch work that looked a lot like the chain rule when doing integration. Likewise, I sometimes saw derivatives with a "+ C" tacked on at the end. This isn't good. You need to be sure that you're completely clear on these concepts, how they're related, and how they differ, as they form the core of this subject.

3) Some people were sloppy with notation. Please don't use the equal sign unless the items are indeed equal. I saw people write things like

f(x) = (x^2+5x) = 2x + 5

which clearly is false. Also, I sometimes saw people do an integral but still retain the integral notation. Not only are these things wrong, but they increase the likelihood that you'll make an error. At some point in your career, you're going to find a grader or a professor who won't allow these notational abuses. I'm not one of those people today, but you do need to be careful!

On a related note, sec(x) and cos(x), etc. are functions. It doesn't make any sense to write 5*cos. (Cosine of what? It's a function.)

4) If you got a score in the 30's, 40's, 50's, or 60's, the time to panic is now. You need to be doing every homework problem and attending office hours and/or the calculus tutoring center in Rowland Hall 416. Note that the tutoring center is open from 9am to 4pm daily. And if you're not attending class, now might be a good time to start. Sorry to bring up some doom and gloom here, but I'm really worried about some of you!

To those who worked hard and prepared, I'd like to thank you and congratulate you. You did a good job on this exam.

Midterm 1 Results and Statistics
Posted Nov. 2, 2004:

Here is the text of the email I just sent to class. Also, please note the grade distribution plot that wasn't in the original email.

Hello, class.

I'm writing to inform you that your midterms have been graded. If you don't have your score yet, please email me, and I will send it to you. I'll also be sending your scores to Dr. Lehman within the hour.

Overall, the scores were very good. Here are the basic statistics for the exam:

1) mean (average) score: 82.22%
2) standard deviation: 17.09%

So in particular, if this were a bell curve distribution of grades, 84% of the class had scores within 1 standard deviation of the mean, i.e., in the range 65.13 to 99.31. 99.5% of the class should be within 2 standard deviations, and 99.99998% should be within 3 standard deviations. However, it doesn't appear to have been a bell curve distribution. EDIT: I made an error here: about 68.3% are within 1 standard deviation, about 95.5% are within 2 standard deviations, and about 99.7% are within 3 standard deviations.

Here are a few comments:

1) Most of you did quite well. Congratulations. I was happy with the performance I saw overall.

2) As I mentioned above, this wasn't a bell curve distribution. Instead, there were two peaks: one with many people with scores from 75 to 95, and a smaller one with people scoring in the 40-55 range. If you were in this lower range, you need to seriously consider what you can do to improve (e.g., attending office hours, working more problems, utilizing the calculus tutoring center, better test-taking strategy, getting private tutoring), or consider whether this is the right time for you to take the course. EDIT: Actually, there were three peaks; I hadn't expected this. For those in the middle peak, keep the faith--you're almost there. Just a little more work, and you'll be over the top!

3) There were a few trends I saw in those who had a harder time on the exam:

a) Scattered work, often combined with very sloppy writing: This made it very difficult to follow your work and assign partial credit. It also made it more difficult for you to catch your errors and made it more likely that you misread and miscopied your work from one step to the next.

b) Work squeezed into a tiny area: This ties into (a) very well. If you need scratch paper, you might consider using the back of the page first and then recopying on the front side.

c) Not a lot of work shown: When you got the problem right, this probably saved you some time. However, when there were errors, it was difficult to assign partial credit, as I couldn't track your progress thorugh the problem. Also, not laying out your steps in a methodical, disciplined way makes it difficult for you yourself to catch your errors. As calculus problems become more difficult, this becomes all the more important.

d) Answers that don't make sense: If you get a negative answer for an area or volume problem, it should be a tip-off that you have made an error in your work. Likewise, if you're finding the area under a curve that never goes above 3 over the interval [0,1], then it should have an area of no more than 3. So, if you get an answer of 40, it should again be a clue to go back and check your work. If you wrote out all your steps clearly, it should be easier to find the first step where there was an error and fix the following steps.

Again, overall, congratulations, and best of luck as we continue this quarter.

-- Paul Macklin
TA for Math 2B, Sections 80 and 81
UCI Dept. of Mathematics