Why does calculus work?

N

NRS

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Sep 14, 2009
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This is a question that's been plaguing me now for a while, sure I can learn how to do integrals and derivatives and limits... (and whatever other instruments of torture are stored up for me now that I'm in Calc II :shock:) I'm hunting for more than proofs, something more litterary. I tried googling, but I'm not too skilled a googler (is that a word?) and couldn't find anything. Any suggestions? I don't really care how dry and uninteresting it is, just as long as it's clear and I can learn from it relatively easily.

Thanks in advance!
Nick
 
I'm not sure what you're looking for. Do you want to understand why it works, or do you want to know what it's good for? If you want the fundamentals try reading Newton and Leibniz. You want dry? That's dry. There are a number of books about math history that will explain what it's all about and how these geniuses thought it up. Math history can be good reading. I'm sure there are plenty of books in your school library. This isn't bad.

Once you get into calc III, it'll really start making sense. You start working in 3 dimensions and you can actually see what's going on. Diffeq, if you really get it, will explain how things really work, especially in 3 dimensions. The math can get crazy. Most of the useful math is computational however. I use programs that solve Schrodinger's equation in 3d all the time.
 
I'm looking for why it works... And I will agree with you that math history is interesting :D
He He He, I wasn't quite going for Newton and Leibniz, though if I get desperate enough, I may end up attempting it. It is encouraging, that I'll understand more in calc 3.

Mostly what I was wondering about was why integrals work, How making an antiderivative is the same as an infinite summation, though the rest of calculus wouldn't be bad as well...

thankyou for your time.

Nick
 
?

Chat up your local librarian. I find that they are skillful in rooting out books dealing with technical subjects but written in layman's terms.
 
Have you taken any physics classes? Calc based is better for what you want to understand, but not necessary. I think you will have a better understanding of "why calculus works" when it is applied to real things. That's the whole reason math was invented in the first place. Newton invented calculus so he could describe the physical universe.

For example when you want to know what the distance is, given velocity and time, you plot velocity vs time and find the area under the curve (or line); that's an integral. You don't need calculus for that, but calculus lets you do it without the graph. The instantaneous slope of that curve/line is the acceleration.

ie. plot a simple graph with the data:

V = 10, 20, 30, 40...etc
t = 1, 2, 3, 4....etc

Now, when you graph it, you'll get a triangle. Find the area of the triangle using geometry. Next, set it up as an integral.

V(t) = dD/dt ; D is distance

dD = V(t)dt find the function V(t).....it's V(t) = 10t

Evaluate the integral for whatever time limits you used on your triangle. You will get the area of the triangle.

There are some good math history books that go into great detail as to how Newton and/or Leibniz came up with it and how/why it works.

Seems like the better question is HOW it works as opposed to WHY. WHY is because that's the way the universe works. Or, that's how God made it.
 
Thankyou, I didn't think I'd recieve this much feedback on such a question :D

mmm4444bot, I'll be at my college library soon, although its a bit small.

tutor_joel said:
that's how God made it.
Click to expand...
The simple answer for everything! :D

Thankyou for taking time to write so much, I am very much looking forward to physics with calculus (I was looking forward to physics before I even knew what calculus was!) Anyway, I just love to find out how and why things work. That's why I've enjoyed calculus soooo much, I feel like I'm getting a look into the inner workings of the universe! :D

I will have to talk to my math proffesor, I think he would welcome a question like this and could also point me in a good direction.

Once again, thankyou!
 
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