Setting up functions with Heavisides to make Laplace transforming easier
In this video, I introduce Heaviside functions and show how to use them (using two different methods) to represent piecewise functions. The first method is easier to carry out but the second method gives a better form for taking Laplace transforms.
Пікірлер: 21
great explanation, thanks!
great explanation
Thanks for the video! In the first example, would the last term of heaviside functions (u3-u4) be subtracted instead of added onto the equation since it is dropping at t=3?
@ericcytrynbaum
2 жыл бұрын
I included the minus sign in the function (4-t) so your suggestion would be correct if you changed that to (t-4).
Nice explanation
I can't get the slopes part & substracting part
Is it possible to write a ramp than increases from 0 whenever f(x) it's 0?
@ericcytrynbaum
Жыл бұрын
I’m not sure what you mean.
@gradozero8140
Жыл бұрын
@@ericcytrynbaum Thank you, I would like to create an Heaviside H(x) function that creates an increasing ramp whenever another function f(x) composed by irregular impulses is = 0. This is for tracking the timing between the impulses (the maximum of the ramp=time between the two specific impulses). However, I'm struggling in trying to make the ramp starting from 0, because the easiest way is to make the Heaviside = x whenever f(x) is equal 0, but in this case, the ramp starts from the actual value of x and not from 0. I would have to subtract something but I don't know what, because this is not known in advance, and if I would already know the spacing between the impulses, I wouldn't need the ramp ...
@ericcytrynbaum
Жыл бұрын
@@gradozero8140 If the impulses are at times t_i, then maybe you want something like this: g(t) = sum over i of (H(t-t_i)-H(t-t_{i+1}))(t-t_i) ?
@gradozero8140
Жыл бұрын
@@ericcytrynbaum Thank you very much. It seems this fits well for regular impulses. But if the impulses are not regular, I'm trying to find a rule to make the ramp starting from 0 whenever f(x)=0 like H(x)=[f(x)
Well done, I like the explanation!
Gracias
there were no laplace transforms in this video. thanks by the way
@ericcytrynbaum
7 жыл бұрын
Good point. The title is a bit misleading, I guess.
H(1-|t|) explanation please
@ericcytrynbaum
3 жыл бұрын
This didn't appear in the video but it's just a slick way of writing a function that is 1 for -1
The title sucks, indeed. but the content is great, thanks!
@ericcytrynbaum
2 жыл бұрын
Good point. Changed.
unfortunetly, you havent taught us really.and you have done it probably intentioanally.
@ezzaddinal-soufi3101
2 жыл бұрын
he made this Video not for u , so be nice if u dont unterstood what he did