There probably isn't and I'm just being silly. But on chapter 14 page 25 example it says that P(i) = j/i. Therefore the convexity is P''(i)/P(i). However instead of 2/i^2 I keep getting [2j/i^3 - 2/i^2]*i/j which does not equal to 2/i^2! I've tried product rule and quotient rule but I keep getting the same answer I think either the notes are wrong or I'm wrong (which is most probable) for calculating P''(i). For P''(i) I get 2j/i^3 - 1/i^2 - 1/i^2 so P''(i) = 2j/i^3 - 2/i^2. Can anyone confirm this? There is most probably a sign muddle up as if I got 2j/i^3 - 1/i^2 + 1/i^2 then P''(i) would = 2j/i^3 (which is correct when you multiply by i/j) Please help.
I don't have your notes in front of me, but the given solution works if (and only if) j does not depend on i and can be treated as a constant: P(i) = j/i P'(i) = j'/i-j/i^2 P''(i) = j''/i-j'/i^2-j'/i^2+2j/i^3 If j does not depend on i, j'=j''=0 and hence P''(i)/P(i) = 2j/i^3 * i/j = 2/i^2 On a totally irrelevant note, ActEd, any chance of getting jsMath installed on the forum? Cheers, Calum
Yes the j is a constant (it's the amount of money being paid at the end of each year). So we're really just differentiating 1/i = i^-1. Times by the power and drop the power by 1 gives -1i^-2 and then +2i^-3. No need for product or quotient rule here. On a side note - if you ever have to differentiate an annuity - it'll be much easier differentiate to the series than use the product rule: eg a_n = v + v^2 + v^3 + ...+ v^n d/di a_n = -v^2 - 2v^3 - 3v^4 - ... - nv^(n+1)
Have asked the IT guys - they say it requires TeX code - which might not be brill for students... Would take 1-2 days work by our guys to get it on the forum - unfortunately they're a bit swamped with other activities at the moment - but thought I would let you know that we're at least investigating the options! Thanks for the suggestion!
I've actually set it up myself, it's surprisingly easy. Yes, the TeX can be scary, but even if people only ever use it to produce subscripts and exponents, it would double the readability of a lot of what we do here. It might even encourage people to post and respond to more technical queries if it becomes easier to present more complex stuff
Having multiple options never hurts. Those who can use it will, those who can't are right where we are now. I'm sure a short sticky on usage will go a very long way, even if it's only for superscripts and subscripts (which can't be that difficult - if you want a^b type ... and change a and b) Don't forget you can upload scanned images of old fashioned pen and paper.
