In the Euler's Method section of my textbook, there are two equations mentioned (see attachment). I was wondering if there was any difference between the two, or if they refer to the same thing.
The help would be appreciated
They are different equations the second being more general than the first.
In we are ignoring the fact that t is a continuous variable and just looking at specific points, , , etc. separted by distance h along the t axis.
In we are retaining the continuity of t- here t could be any number. Of course, if we take to be some specific value, then define , , , , , etc. then the second equation becomes the same as the first.