From a systems optimization position, we quite often DO NOT know the function that characterizes our system, we can only take samples which will provide us with f(x) and f(x+_dx). So it is much more often the case in practice (rather than in mathematical theory) that we will ONLY know three data points and attempt to characterize around a central point using this formula. That is why we learn this, teach this, and use this in real-life systems.
Regarding central difference, why not just use fwd difference for the first point and then use central difference until the penultimate point when use backward difference for the last point?
Question, isn't the whole point of these methods that all you have are data at discrete points and that you almost certainly DON"T know function. But you know the data at each point. So you know the function value AND the value of the independent variable, and that's why you would use these techniques. If you have the analytic form of the function and it's easy to compute, then yeah, there's no point in using these techniques...
best numerical methods videos on youtube!!! i dont know why you dont have more subscribers
From a systems optimization position, we quite often DO NOT know the function that characterizes our system, we can only take samples which will provide us with f(x) and f(x+_dx). So it is much more often the case in practice (rather than in mathematical theory) that we will ONLY know three data points and attempt to characterize around a central point using this formula. That is why we learn this, teach this, and use this in real-life systems.
Great video. Really explained it well
Regarding central difference, why not just use fwd difference for the first point and then use central difference until the penultimate point when use backward difference for the last point?
Great explanation.
thank you sooooo much for this playlist!!!
this is great but
how can we derive the third derivative finite difference
How to calculate nth derivates?
Question, isn't the whole point of these methods that all you have are data at discrete points and that you almost certainly DON"T know function. But you know the data at each point. So you know the function value AND the value of the independent variable, and that's why you would use these techniques. If you have the analytic form of the function and it's easy to compute, then yeah, there's no point in using these techniques...