Comments on: It’s Mathemagic! http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/ Otherwise known as "I couldn't think of a clever title." Fri, 21 Nov 2008 04:03:45 +0000 http://wordpress.org/?v=2.5.1 By: Cap’n Refsmmat’s Blog of Doom » Bored Students: Unite http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-6541 Cap’n Refsmmat’s Blog of Doom » Bored Students: Unite Tue, 19 Aug 2008 02:58:41 +0000 http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-6541 [...] often blogged about education in the past. As I am a high school student, it’s a topic that’s rather [...] [...] often blogged about education in the past. As I am a high school student, it’s a topic that’s rather [...]

]]> By: Cap'n Refsmmat http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-44 Cap'n Refsmmat Fri, 22 Feb 2008 04:59:25 +0000 http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-44 $latex F(t) = 6x$ $latex f(t) = \frac{d}{dx}F(t) = 6$ Let's suppose f(t) is a function giving the velocities of some object, and F(t) represents its position at any given time t. Suppose I'm asked to find the distance traveled by the object from t=2 to t=4. That would be $latex \int_2^4 f(t) dt$ correct? (The integral of velocity is position -- if you find the area under a velocity graph, you'll end up with how far the object went. Try it.) With this problem we can see that the answer is 12. But if the integral was harder to do, we'd use the antiderivative of f(t) (F(t)) to solve. The distance traveled by the object is its final position minus its initial position, and F(t) tells us the object's position -- meaning that F(4) - F(2) is the distance traveled. So, $latex \int_2^4 f(t) dt = F(4) - F(2)$ Make sense? F(t) = 6x
f(t) = \frac{d}{dx}F(t) = 6
Let’s suppose f(t) is a function giving the velocities of some object, and F(t) represents its position at any given time t. Suppose I’m asked to find the distance traveled by the object from t=2 to t=4. That would be
\int_2^4 f(t) dt
correct? (The integral of velocity is position — if you find the area under a velocity graph, you’ll end up with how far the object went. Try it.)

With this problem we can see that the answer is 12. But if the integral was harder to do, we’d use the antiderivative of f(t) (F(t)) to solve. The distance traveled by the object is its final position minus its initial position, and F(t) tells us the object’s position — meaning that F(4) - F(2) is the distance traveled.

So,
\int_2^4 f(t) dt = F(4) - F(2)

Make sense?

]]> By: yourdadonapogos http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-43 yourdadonapogos Fri, 22 Feb 2008 02:25:06 +0000 http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-43 I actually wondered why it worked and no one ever bothered to explain it to me. It obviously works, but why? I actually wondered why it worked and no one ever bothered to explain it to me. It obviously works, but why?

]]> By: swansont http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-20 swansont Thu, 14 Feb 2008 17:20:16 +0000 http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-20 I think part of the problem in introductory physics is that a whole bunch of equations get thrown at the students, and they don't realize how they are all related. When I was TA-ing most students were horrified at my suggestion that they derive an equation. I know that deriving an equation is not a guarantee that one knows what it means, but I think that if you can't, you probably don't have a much of clue about how to use it. I think part of the problem in introductory physics is that a whole bunch of equations get thrown at the students, and they don’t realize how they are all related. When I was TA-ing most students were horrified at my suggestion that they derive an equation. I know that deriving an equation is not a guarantee that one knows what it means, but I think that if you can’t, you probably don’t have a much of clue about how to use it.

]]> By: Cap’n Refsmmat’s Blog of Doom » Ye Olde English... Teaching http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-18 Cap’n Refsmmat’s Blog of Doom » Ye Olde English... Teaching Thu, 14 Feb 2008 05:25:45 +0000 http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-18 [...] else is invented in the next few dozen years. This perhaps ties back to my earlier post about “mathemagic” — the point being that rather than teaching students how to write an essay analyzing [...] [...] else is invented in the next few dozen years. This perhaps ties back to my earlier post about “mathemagic” — the point being that rather than teaching students how to write an essay analyzing [...]

]]> By: Cap'n Refsmmat http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-10 Cap'n Refsmmat Tue, 12 Feb 2008 16:28:56 +0000 http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-10 I think physics takes memorization <em>and</em> understanding. You need to know the equations and how to use them. You just have to be snappy in figuring out which equations will get you from where you are to what you want. That takes understanding of the relationships between variables. I think physics takes memorization and understanding. You need to know the equations and how to use them. You just have to be snappy in figuring out which equations will get you from where you are to what you want. That takes understanding of the relationships between variables.

]]> By: ecoli http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-8 ecoli Tue, 12 Feb 2008 06:46:15 +0000 http://blogs.scienceforums.net/capn/2008/02/12/its-mathemagic/#comment-8 I agree completely. My physics prof the other day told us that we should memorize the physics formulas... why? So we could do better on the MCATs. *sigh* I guess he wants us to understand them most importantly, but if you can't do that, memorization is good enough. Interestingly, my problem with physics has been the opposite. I understand concepts well enough, but applying them is harder. I can't easily memorize equations and I don't have the skills or time to derive them during an exam. I don't have the greatest math skills... what's one to do? I agree completely. My physics prof the other day told us that we should memorize the physics formulas… why? So we could do better on the MCATs.

*sigh*

I guess he wants us to understand them most importantly, but if you can’t do that, memorization is good enough.

Interestingly, my problem with physics has been the opposite. I understand concepts well enough, but applying them is harder. I can’t easily memorize equations and I don’t have the skills or time to derive them during an exam. I don’t have the greatest math skills… what’s one to do?

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