[jack.hadamard]

(Original post by nuodai)
I think this problem is quite contrived for the purposes of setting a STEP question, but it's not completely useless.

I am not convinced Euler knew about STEP at the time.

[nuodai]

(Original post by jack.hadamard)
I am not convinced Euler knew about STEP at the time.

You'd be surprised...

[Dog4444]

This question isn't from the siklos booklet, but I see no point in adding another thread.
I checked the solution to STEP2 1996 Q8 by speleo: http://www.thestudentroom.co.uk/show...51#post8025151
and I can't follow how he guesses what g(x)/h(x) is. And he mentions "aux quadratic" twice and i can't understand what it means.

To make more clearer,
If h(x) = kx, then h(x) = -2x.
So h(x) = Ae^x + Be^-x -2x.

I understand where the first line comes from, and that we get a contradiction, but can't follow how he got to the second line straight away.

Also, when he writes something like this:

g(x) = Acosx + Bsinx + ...
g(x) = pcos2x

I can't follow how he jumps from one to another.

pcos2x doesn't work, because it doesn't satisfy specific values of g(x), but as far as I see, the idea that g(x)=Acosx-2cos2x is the result of a guess, not an analytical approach.

And the last question how would we know that there is a UNIQUE function g(x)/h(x)?

[Slumpy]

(Original post by Dog4444)
This question isn't from the siklos booklet, but I see no point in adding another thread.
I checked the solution to STEP2 1996 Q8 by speleo: http://www.thestudentroom.co.uk/show...51#post8025151
and I can't follow how he guesses what g(x)/h(x) is. And he mentions "aux quadratic" twice and i can't understand what it means.

To make more clearer,
If h(x) = kx, then h(x) = -2x.
So h(x) = Ae^x + Be^-x -2x.

I understand where the first line comes from, and that we get a contradiction, but can't follow how he got to the second line straight away.

Also, when he writes something like this:

g(x) = Acosx + Bsinx + ...
g(x) = pcos2x

I can't follow how he jumps from one to another.

pcos2x doesn't work, because it doesn't satisfy specific values of g(x), but as far as I see, the idea that g(x)=Acosx-2cos2x is the result of a guess, not an analytical approach.

And the last question how would we know that there is a UNIQUE function g(x)/h(x)?

Do you have the question nearby?
Edit-and a quick look at his solution suggests Aux Quadratic means auxiliary quadratic (a term used in solving 2nd order ODEs-it's possible you refer to it as something different?).

[Dog4444]

(Original post by Slumpy)
Do you have the question nearby?
Edit-and a quick look at his solution suggests Aux Quadratic means auxiliary quadratic (a term used in solving 2nd order ODEs-it's possible you refer to it as something different?).

I don't know. I've never see 2nd order ODE before.

[Slumpy]

(Original post by Dog4444)


I don't know. I've never see 2nd order ODE before.

Right...it may be worth doing a bit of work on 2nd order ODEs before trying to do STEP questions on them. The question in question (fabulous turn of phrase if I do say so myself...) doesn't look too bad, but if you've never done 2nd order ODEs, it won't be the best place to start!

[Dog4444]

(Original post by Slumpy)
Right...it may be worth doing a bit of work on 2nd order ODEs before trying to do STEP questions on them. The question in question (fabulous turn of phrase if I do say so myself...) doesn't look too bad, but if you've never done 2nd order ODEs, it won't be the best place to start!

There was a syllabus change in 1994, and 2nd order ODE are not in A-level (non-further) syllabus. So, it's quite weird. I guess, it's a good idea to know it, anyway.

[Slumpy]

(Original post by Dog4444)
There was a syllabus change in 1994, and 2nd order ODE are not in A-level (non-further) syllabus. So, it's quite weird. I guess, it's a good idea to know it, anyway.

Ah. I didn't do A levels so didn't do that. I'd say if you want to do STEP, it's very much worth doing FM (although I was under the impression that STEP I and II had the syllabus of just a single A level), and definitely learn ODEs, just because they're great anyways.

[Dog4444]

Another one:



I did manage to get the whole thing, but did the second part by manipulating with all these brackets.

Can't follow this:



I don't understand where that b come from and as the result I can't follow what Siklos did afterwards.

[DFranklin]

He is defining b_n to be the nth term of the original series. (i.e. ).

[Disclaimer: haven't actually done any calculation; it's possible there's an off-by-one in what I wrote].