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
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.