The Student Room Group
Reply 1
Divide both sides by r(1-r^2) so you can do seperating the variables on this differential equation.
Reply 2
:ditto:

That's what I got. You just need to solve for r in terms of t at the end.
Reply 3
Rather than share answers, it'd be better if you kept it to helpful hints.
Reply 4
Nice work insparato.
Reply 5
Lusus Naturae
Nice work insparato.


Thank you :smile:, as of SsEe request though i deleted my answer and gave a push in the right direction.
Reply 6
Next question...

I might as well link to the problem sheet:

http://www.maths.ox.ac.uk/current-students/undergraduates/lecture-material/Mods/analysis1/pdf/analysisI7.pdf

I'm stuck on 3(c) and 4 at the moment. Any suggestions?
jamesgurung
Next question...

I might as well link to the problem sheet:

http://www.maths.ox.ac.uk/current-students/undergraduates/lecture-material/Mods/analysis1/pdf/analysisI7.pdf

I'm stuck on 3(c) and 4 at the moment. Any suggestions?


3 c)

Use the Binomial Theorem followed by Upper Negation. Ill give a full solution if you want it.
Reply 8
I've never heard of upper negation. I think we're meant to do it by using multiplication of series. As SsEe says, I guess we won't learn much if you give away the whole answer, but a point in the right direction would be nice. I'm guessing we need to use results from parts (a) and (b).
Reply 9
jamesgurung
Next question...

I might as well link to the problem sheet:

http://www.maths.ox.ac.uk/current-students/undergraduates/lecture-material/Mods/analysis1/pdf/analysisI7.pdf

I'm stuck on 3(c) and 4 at the moment. Any suggestions?


Way past my level :biggrin:. Doubt ill ever get that far mathematics wise.
http://binomial.csuhayward.edu/Top10.html
here is some explanation of upper negation...
Reply 11
Catalog #: 3900000

Known as: The Bloody Binomial Theorem

:cool:
Reply 12
Now I realise that I'll sound like a real jobsworth when I say this, but: don't you guys think it would be better just battling with the problem sheets on your own? And if you really, really need a hint with something (instead of leaving it to a supervision) just popping round one of your mates and mulling it over?

It's just that the problem sheets are meant to be problematic (funnily enough!). And I honestly believe you get more out of these things if you battle with them yourselves rather than turning to others. I know people are only giving hints, but in the majority of these type of problems, you only need one "hint" and the rest is just turning the handle.

I think it's commendable that you guys are so organised and all giving each other support towards your maths at Ox, but I can't help but think that this is the wrong way to go about things. By all means shoot me down for being a nob about the whole thing, but as I said earlier - these things are far more rewarding if you persevere on your own. Not only that, but you don't lull yourself into a false sense of security come exam time: "I answered everything on that problem sheet, so don't need to go over that area too much" rather than "I answered 3/4 of that sheet, so need to spend a little time trying to understand why I couldn't do the last 1/4 and get on top of the relevant material/ideas".

Maybe instead pose questions on here that are from relevant books? That way you're all getting practice, but not giving away anything on the official problem sheets? Anyhoo - just thought I'd say; feel free to totally ignore me!

:smile:
Reply 13
Wrangler
Now I realise that I'll sound like a real jobsworth when I say this, but: don't you guys think it would be better just battling with the problem sheets on your own? And if you really, really need a hint with something (instead of leaving it to a supervision) just popping round one of your mates and mulling it over?

It's just that the problem sheets are meant to be problematic (funnily enough!). And I honestly believe you get more out of these things if you battle with them yourselves rather than turning to others. I know people are only giving hints, but in the majority of these type of problems, you only need one "hint" and the rest is just turning the handle.

I think it's commendable that you guys are so organised and all giving each other support towards your maths at Ox, but I can't help but think that this is the wrong way to go about things. By all means shoot me down for being a nob about the whole thing, but as I said earlier - these things are far more rewarding if you persevere on your own. Not only that, but you don't lull yourself into a false sense of security come exam time: "I answered everything on that problem sheet, so don't need to go over that area too much" rather than "I answered 3/4 of that sheet, so need to spend a little time trying to understand why I couldn't do the last 1/4 and get on top of the relevant material/ideas".

Maybe instead pose questions on here that are from relevant books? That way you're all getting practice, but not giving away anything on the official problem sheets? Anyhoo - just thought I'd say; feel free to totally ignore me!

:smile:


I agree, it would be completely wrong if this thread became the complete answers companion to the sheets found on www.maths.ox.ac.uk . Struggling with problems is a very important part of learning. Getting stuck, being forced to break off and reapproach is one thing, but there does come a point when going round in circles and not getting anywhere stops being productive and some advice or hints is the best way to improve.

Correct me if I'm wrong, but are people doing last terms problem sheets at the moment as preparation for collections or something? Getting help for this is totally acceptable to me if you are happy that that is the way you think we help you prepare the best. Even so, it's probably better to take the problems that you're really stuck on to one of your tutors between going up and collections, they should be able to give you time and help, and are probably not going to teach you bad answers, bad information and bad habits that you might get from "some random bloke off the internet".

Getting help for weekly problem sheets that you are going to be assessed on as your own work is unfair on your fellow students in the short term, but unfair on yourself in the long run.
Reply 14
I didnt mean for this thread to be a list of all the answers, just a place for discussion about the some of the problems people have found particuarly challenging.

I agree that spending the time, yourself working on a problem helps to give you a much better understanding, but also if you've spent say, over 7 hours on one question that you must be missing something and it might help to talk it over with someone.

On that point, if anyone could give me a hint on how to evaluate the last infinite sum on the analysis sheet it would be a great help. I cant see the link between it and the first parts of the question, thanks (the link for the sheet is on one of the above threads).
Reply 16
assume you mean the sum with 27^n in it. Think about the z term in the expansion of e^z
Reply 17
insparato
Divide both sides by r(1-r^2) so you can do seperating the variables on this differential equation.


I'm also working on this question. I think i've got r and theta in terms of t but I don't know how I now sketch the phase paths. If I eliminate t will I get the equation of the phase path? However this seems too complicated to sketch. Also in my equations for r and theta do I need to eliminate the constants of integration? Thanks :smile:
Reply 18
I'm also really struggling with this question:

A particle moves on the smooth inside surface of the hemisphere z = &#8722;sqrt(a^2 &#8722; r^2), r <= a,
where (r, &#952;, z) denote cylindrical polar coordinates, with the z-axis vertically upward.
Initially the particle is at z = 0, and it is projected with speed V in the &#952;-direction.

a)Show that the particle moves between two heights in the subsequent motion, and find
them.

b) Show, too, that if the parameter &#946; = (V^2)/4ga is very large then the difference between
the two heights is approximately a/2&#946;.

a) Using conservation of energy I found that the particle moves between z=0 and z=[(V^2)+sqrt{(V^4) +16(g^2)(a^2)}]/4g but I am not at all confident in this answer.

b) Substituting in the parameter I get 2&#946;a not the correct answer. This makes me believe I have gone wrong in part a.

Any advice on how to attempt this question/the correct answer would be great. I can supply more details on what I have tried if necessary.

Thank you.