Hi everyone! Is anyone willing to watch a Khan Academy video about the Unit Step function and Laplace transforms with me so I can ask specific questions at different time stamps? I am really trying to understand how adding and subtracting different functions make the graph jump around. Thanks! :o)

Question

anonymous · Answer

Here is the video starting at 2:58 https://youtu.be/4Mr7aEHQr8E?t=2m58s

anonymous · Answer

Please stop watching the video at 4:48

I totally get why the function is at 2 up until he gets to "pi", my first question is this:
If you were to put it into simple words, what exactly does the minus sign tell the graph to do? I have heard people say that the minus sign "kills" the function, like it doesn't exist anymore and you start with a new function that comes right after the "minus" sign, but that can't be true because if it were true, he could have just written 2-Usubpi(t), but actually he had to write instead 2-2Usubpi(t), so it doesn't seem like the whole "kill" explanation is true.
I suppose we can start with that question and work our way forward. Thanks :o)

parthkohli · Answer

It follows from the definition of the unit step function.

parthkohli · Answer

We want to define a function that is 2 upto $\pi$ and 0 beyond that. For that, we exploit the unit step function, which is 0 till one number and 1 beyond that.

anonymous · Answer

okay... so let me see if I understand...

anonymous · Answer

if you were to graph the unit step function by itself, it looks exactly like khan shows it, it is zero up until "pi, then it skips to one...

if you were to just subtract the unit step function, the the minus sign simply instruct the graph to forget about the stuff "before" the minus sign? Like if you had 2-Usubpi(t), would you get something that looks like this?|dw:1431534748739:dw|