# Does anybody understand the concepts of Calculus?

1. Jun 22, 2006

### Revolver

I can learn how to do the problems, but I never understand why I'm doing the problems. Exactly what am I proving or figuring out? I can do derivatives, but I really don't know what a derivative is, I just know how to solve a derivative problem. How do you figure the logic? I swear, Calculus was devised by Satan himself :)

2. Jun 22, 2006

### chroot

Staff Emeritus
Sounds like you have a rather bad teacher. Perhaps you should pick up a book like "A Tour of the Calculus" by Berlinski for a deeper understanding of the motivation behind calculus. Calculus is, in fact, an essential tool in almost every scientific or engineering pursuit.

- Warren

3. Jun 22, 2006

### fargoth

uhm, you got confused...
the time integral of acceleration is velocity, and the time integral of velocity is displacement....
the time derivative of displacement is velocity, and the time derivative of velocity is accelrration...

and in other words, the change rate in time of displacement at a certain time would be it's velocity on that specific time - this change rate is the slope of the x-t (displacent as Y an time as X) graph..
(and the change rate of velocity is acceleration - so the second derivative of displacement would give you acceleration)

and if you know the velocity at every moment summing it up over time (integrating it) would give you the total displacement.

you can see what derivative does if you look at it's definition:
to determine the slope of a line, you take it's Y value at point a -meaning f(a)
and at another point b -meaning f(b), you subtract f(b) from f(a) to get the height difference of the point and you devide this height difference by the distance between a and b.
now, derivative does the same, only it take two very close points and check the slope between them:
$$\frac{f(x)-f(x+\Delta x)}{\Delta x}$$
where $$\Delta x$$ is very very small.
and this is how you get the tangential line's slope of a curve at point x...

Last edited: Jun 22, 2006
4. Jun 22, 2006

### Hootenanny

Staff Emeritus
Bloody Hell, I know the wrong way round! can't believe I did that!!! Time to catch some Z's :zzz: :zzz: :zzz: I'll delete my post because I haven't got time to edit it.