Integral physics, me understand a thing with respect to integration

[christian0710]

Hi, I'm trying to understand why

When you write a*dt = dv then you can write the integral like this.,

∫dv (from v0 to vt) = ∫a*dt (from 0 to t)

My challenge is this: from the equation a*dt = dv, the term "dv" geometrically means an infenitesimalle small change in function value of the function v(t), so dv must be an integer. So you are integrating an integer, dv, and the graph of an integer is a straight horizontal line on the v(t) vs t axis. so is it correctly understood that if we assume dv= 1 then the integral of dv should just be v. But here is the part i don't understand, the lower and upper bounds are v0 and v, usually the limits of integration are limits on the x-axis and Not on the Y-axis (or V(t) axis), so should i interprete dv as an integer whose function has Velocity on the x axis? This just does not make sense to me,

Here is a photo of what is written in the book.,

 

[mathman]

dv must be an integer

Absolutely no.

All the equation is saying is that the change in velocity is the integral of the acceleration.

 

[jtbell]

so dv must be an integer

Why do you think that?

and the graph of an integer is a straight horizontal line on the v(t) vs t axis

Are you perhaps confusing the words "integer" and "constant"?

 

[Svein]

dv = a*dt just means that an acceleration creates a change in velocity. The amount of change can be calculated using integration (or in the simple case, where the acceleration is constant, multiplying the acceleration by the time passed).

 

[PWiz]

The equation can be rearranged to give you $a=\frac{dv}{dt}$ , and dividing two infinitely small numbers results in a definite one($a$ over here). Note that both $dv$ and $dt$ mean changes in the respective quantities over an infinitesimally small interval, and this in no way suggests that they always equal to an integer. It appears that you've misunderstood the concept of the $dx$ terminology, so I recommend that you go through this article: http://www.felderbooks.com/papers/dx.html

 

[Svein]

an infinitesimally small interval

I always thought that "infinitesimals" concept died out around 1880...

 

[PWiz]

I always thought that "infinitesimals" concept died out around 1880...

With the $dx$ notation, yes.

 

[SteamKing]

I always thought that "infinitesimals" concept died out around 1880...

Maybe for certain schools of pure mathematicians, but the infinitesimal concept was revived in the TwenCen to serve as a basis for calculus and analysis.

See:

http://en.wikipedia.org/wiki/Infinitesimal

As you might have noticed, infinitesimals still heavily populate texts on physics and calculus, among other subjects.

 

[Svein]

Well, having the equivalent of a Master's in complex analysis, that makes me a "pure mathematician", I suppose.

 

[PWiz]

Well, having the equivalent of a Master's in complex analysis, that makes me a "pure mathematician", I suppose.

Well I haven't even finished high school yet, makes me feel a tad bit insecure haha