Submitted by David Lee on Mon, 03/19/2018 - 17:22
Forums:
Enjoyable assignment on series etc. With regard to warm-up question (i)(b), I noticed that a first term of 0.75 is problematic in that it yields a third term of zero and I thought this might merit some comment within the assignment itself or within the feedback notes.
Thanks
Thanks for your comment - I will have a good look at the assignment later today or tomorrow.
Dodgy starting points
Thanks again for your comment, I will change the feedback for this assignment to note that some series can have problems with certain starting points.
For this one, I agree that a first term of $\frac 3 4$ is problematic, as is $\frac 2 3$ and indeed a first term of $0$!
You can find (some?) of the problematic staring points by using the iteration
\[
t_{n+1} = \frac 4 {6-t_n}
\]
with a starting value of $t_1=0$. I am not sure yet if this will find all the possible dodgy starting points or just some of them!
Dodgy starting points
Thank you for your response. I find that the first 5 terms resulting from the proposed iteration are 'problematic' starting points, but after that, convergence to the stable limit from the trial problematic starting point returns, with these later starting points being equal to, or very close to the unstable limit. I should point out that my interest in the STEP assignments is as a retired aeronautical engineer with some background in introducing STEP to FE College students over 20 years ago - since then I have been training flight test professionals and have had some interest in 'sensitivity analyses' i.e. how sensitive is an 'answer' to assumptions about a starting point to a problem. It just struck me as I worked (recreationally) through this assignment that this particular problem was a good example of 'sensitivity issues' in problem solving, including difficulties and uncertainties when utilising EXCEL or similar - I think it is beneficial for such uncertainty to be highlighted to students. Please don't feel that further comments on this point are required, unless you really feel the need. I think that your proposed note in the assignment feedback to highlight uncertainty arising from different starting points will be helpful. I wish this facility had been available to me and my students back in 1990's! You are doing a great job. Keep it up. Thank you.