William Matheson (nova_one) wrote,
William Matheson

calculus update

Alright! The midterm’s in the can – I certainly passed – and my assignment for Monday is done, too, so there’s a ridiculously unfettered weekend lying ahead of me. And a friend’s having a birthday, so that works out pretty nice.

So far I’ve enjoyed – well, OK, as much as one can possibly enjoy – taking calculus at Dal. There’s one fellow who’s a graduate student in the field of number theory and he staffs the learning resource room – which is in a horrible temporary location in the LSC, but at least there is one – and he is very helpful, because he actually cares about helping people, and because his explanations are clear. Not all of them are like that, but at least they’re there.

And the prof is a likable, funny guy, too. There are lots of good profs – for me, I judge them partly by how much I hear their voices in my head when I’m trying to solve a problem. (No, I am not on any sort of medication.) This one is full of important math maxims.

Also, when he brings his car, he offers me a lift back to his neighbourhood so I can catch my bus. That saves me about an hour or more of messing around trying to get other busses to get out to it. Tonight we deconstructed the midterm a bit – well, my performance on it, to be specific – I’m embarrassed by the fact that I missed a few questions that were taken straight from the class notes, but I do feel like I’m on the up and up in terms of understanding.

And the bus driver tonight was the chatty fellow that I’ve spoken with off-and-on over the past year. It was good to see him again, and it put a nice topper on my largely successful day. I think I studied about as much as I humanely could. I looked for opportunities and I took action.

Some LOLz:

- A guy in the help room an hour before we start the midterm, speaking to the grad student: “So, do you have any general tips about calculus?” Actually, it's not a bad question, but it just sounds an awful lot like he left off doing problems until the last microsecond.

- There was an engineering student who apparently didn’t know that anything^0 = 1. (Well, at least I’m in good company. That was me not so very long ago.)

Let me digress. Here are some helpful facts about exponents.

You know that 2^2 = 2 * 2 = 4 and that 10^2 = 10 * 10 = 100. This is from the basic rule you know:

1. a^n where n is any positive whole number means multiply a by itself enough so that you see it on your paper n times [e.g.: 2^4 = 2*2*2*2 = 16]

2. anything^0 = 1 [e.g.: 99999999999999^0 = 1]

3. anything^1 = that very thing [e.g.: 99^1 = 99 … Think of it as 99 * … oh, I’m done already.]

4. anything^(-n) = 1/(a^n) [e.g.: 10^-1 = 1/10 = 0.1 … 10^-2 = 1/(10^2) = 1/100 = 0.01]

Back in rule 1, I could have said that n could be any whole nonzero number. Why? 10^-2 = (1/10)*(1/10) = (1/(10*10)) = 1/100) But separating the ideas makes it easier.

5. anything^(g/h)

This needs a bit of explanation. The h will be the degree of your root. You’ll probably see 2 the most, that’s the square root. You may also see 3 (cube root), 4 (fourth root), or more. Those will have a little 3 or 4 next to the check symbol. Square roots are so ubiquitous that we don't bother with the 2.

The top value acts just like n did before, but it’s all inside that root.

[e.g.: 4^(1/2) = the square root of 4^1 = the square root of 4 = what multiplies by itself once* to make 4 = 2]

[e.g.: 2^(7/4) = the fourth root of 2^7]

[e.g.: 2^(-7/4) = 1/(the fourth root of 2^7)]

I could go on, and on, and on, but these are just some key facts that should be part of your toolkit, if they aren’t already. (I got a university degree and an honours certificate without knowing these things.)

* - You’re multiplying the thing by itself n-1 times, though the items appear on the paper n times, e.g.: 2^2 = 2*2 = 4

- I forgot I was making a list of funny things. We’ll end there.

Y’know, I like math – I just find learning it troublesome and frustrating. I suppose I might also be lazy. I mean, everybody would like to play the double bass in the symphony, but you’re not going to get there just by snapping your fingers.

But seriously – if I can do it (remember, I failed Grade 10 math three times, but that just goes to show that you don’t learn math by my strict regimen back then of sleeping and doodling and chatting as much as I could get away with), you can do it!
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