Several questions arose in the comments from my last post about 18.02 -- Multi-Variable Calculus. Here's a quick rundown on what it is.
If you've had calculus before then you know what an integral is. Basically, if you have a pretty graph like this:
An integral is defined as the sum of the area between the curve and the x-axis. Oftentimes curves go on forever to the left and right, so it's helpful to put some limits on it. So, for example, using the curve above, you could integrate it from a to b (shown below).
All of the yellow shaded area is the portion of the are under the curve that is positive (above the x-axis). The green portion is negative (below the x-axis). Add it all together and you get the integral.
Now that you know what an integral is I can give you a basic definition of Multi-Variable calculus. What would happen if, instead of just being on a flat plane and being just a curve, your graph was a 3D surface somewhere in space?
Instead of just one variable in terms of another (y=f(x), y in terms of x) you now have 1 variable in terms of two others (z=f(x,y), z in terms of x and y). A double integral does something a lot like a single integral except it finds surface area instead of just the area under a curve.
Got it? Ok, I'll leave the explanation of MultiVar at that, but know that there's a lot more to it (like triple integrals (volume), vector fields, partial derivatives, flux, and matrices).
I had an 18.02 test yesterday. I came out of the test not feeling great, but not feeling horrible. It was a decent test, I answered a decent number of questions and I felt like I did decently well. All that was left was to wait and see if I got fail-mail. What's fail-mail? Basically, if you fail a test you get an e-mail that says "Hey, you failed (and suck) and you need to take a make up test. . . or else."
Just kidding, they aren't that mean. The cool thing is that I've gotten two of them so I can kind of pinpoint when fail-mail gets sent. If I don't get any during that window I'm safe. Here are the last two fail-mails I've gotten (click to enlarge):
Using these e-mails I was able to predict fail-mail sometime between 5:30 and 7:30. 9 o'clock came and went and I hadn't gotten an e-mail! This is a very good sign. I decide to check online and see if grades are posted. I go to our math website and see this:
Due to the difficulty of the exam, 5 points have been added to all scores. The scores in the on-line system include the 5 extra points.
Woo-hoo! 5 free points!
I check my grade and see:
YAY! I PASSED! I PASSED A MATH TEST! YAY!
That's the story, I passed my second math test of the year and it was the only test that was hard enough to warrant adding points to everybody's score. The best part is that I still would have passed, even without those 5 points! Math is done until finals folks, 2 weeks away.