Math Is Fun Forum

Well it was y that was confusing me, actually, to be honest - the context of the question is a linear second order ordinary differential equation.

I imagine the first is not true but I don't know. I recognise the source immediately, of course, and JKR uses lots of places, creatures and plants from actual mythology - which may, or may not, have some truth in them. Empirically speaking, most of the myths which she uses are no more than that, but I don't really want to get drawn into a debate over the existence of the Loch Ness Monster or Atlantis or other pieces of mythology. Anyway, one of her great skills was in taking these creatures of myth and legend and putting her own spin on things so, whether any of her potions would actual do anything, if their ingredients even exist in some cases, I find doubtful. As for the second, again, whether they have healing powers I don't know, but I'm inclined to think not. They may do though - I highly doubt that they would be a cure to most common poisons, but much of western medicine is based on extracting compounds from plants and animals, so there could be some medical truth in it. The last one is definitely true, though, the aconitum genus goes by many names, including aconite, monkshood and wolfsbane. I imagine the last name comes from the fact that many species of aconitum contain aconitine - a powerful neurotoxin, which would probably kill many actual wolfs - (hence wolfsbane - the bane of wolves) which would give rise to the legend of it being toxic to werewolves, etc.

Hi bob bundy

This little site is really handy - http://detexify.kirelabs.org/classify.html

You have to be quite good with a mouse though, mind you . Otherwise, there is a manual for all of LaTeX, which includes a maths section here - http://en.wikibooks.org/wiki/LaTeX/Mathematics - and the detexify site has a link to a huge pdf full of just about every symbol which LaTeX supports, but that is even more cumbersome. Sites such as codecogs can also help, since their buttons will provide the control characters for you and wikipedia is typeset in LaTeX so you can right click on any maths which includes the symbol which you want and view the source, or simply click on edit and the LaTeX will appear for you to look at. Usually the control sequences are quite high-level (which means that they read like natural language, so sometimes you can have a pretty good guess. I'm sure I don't need to tell you what \overrightarrow{AB} does .) This means that it's quite easy to pick them up if you want to use LaTeX more often, for example, I have always done my maths homeworks in LaTeX which meant that I got used to it very quickly. For typesetting on here, though, those methods will provide quick answers.

As for using an editor, it's much easier when typing maths on maths is fun to just stick the code in directly, rather than copying and pasting across, however, if you do want to use it for documents or for personal use off-site then I would highly recommend a proper text editor, but that really is getting into personal use, you will need the LaTeX libraries and other such things, whereas mathsisfun does all of that natively.

Hi guys, I'm sorry that this argument has sprung up unnecessarily, and I feel that I am largely responsible for recommending the creation of a new thread. The reason for this being that my understanding of the 'crash course' thread over in the help forum is that it is a guide for using LaTeX on this forum in order to help users of this forum to make the most of it and make the maths on it nice and clear so that people don't become confused with expressions like 'x + 2^3 + x' and to avoid the necessity for lots of brackets and so that people can input summations and integrals and other such things with greater ease. I hope that I am right in thinking that anonimnystefy is quite interested in TeX's much wider use as a typesetting language for entire documents. Indeed it is frequently used in scientific papers and even in published books and one can use TeX for much the same things that many people use Word, or Pages or any other word processor for. I merely thought that he may be interested in seeing how this can be done and also in practising his LaTeX for this forum, which I think he said that he was having trouble with (I'm sorry anonimnystefy I don't want to speak to you I just wanted to make clear why I gave the advice that I did.) In short I didn't want to clog up the 'crash course' with an advanced manual in LaTeX and since this forum doesn't seem to have any 'private message' function, I thought it might be nice if anonimnystefy could start a dedicated thread. I, too, however was worried that this was somewhat beyond the scope of our maths forum, TeX is a mark-up language which happens to have some nice maths support, but it's really not what this forum is about. I didn't mean to cause an argument and I see bobbym's wisdom. If you would think it better, bobbym, then I would be happy to help anonimnystefy by e-mail or something. Understandably, however, I did not suggest this at first because I wouldn't wish to hand out my personal e-mail address on a public forum, so if that is to be the case then I shall create a dedicated address for it.

Hmmm, yes I see, but ought we not account for it. I tried taking the four outside, although perhaps that was not correct. What I am interested in, though, is why we don't have to worry about it when computing a,b,c,d,e and f

Oooh thanks bobbym that's perfect, my only question would be where we've accounted for the fact that the product of our denominators is four times the original denominator. I also wonder if it would be possible to tell that our numerators would be quadratics if we hadn't had the answer to begin with - more out of curiosity than anything else.

Hmmm, I can definitely do 2) in theory - although that's not to say that I might not have some trouble with doing a large, difficult, practical example - although I should think I would probably enjoy trying and, well, as for 1) I not only know the form, I know what they are, since I wish only to verify it, as much as I would like to be able to derive something like this - not being a computer - or at least an extremely experienced and intelligent professor of advanced mathematics - I think that to do so may well be somewhere beyond me.

Where I am stuck is with regards to where to go with these 2 pieces of knowledge.

Wow, I see, okay thanks bobbym, I was just interested mainly in a quick look at the proof and I agree that I don't think there's much that a human could do with a pen and paper, but since you seemed to have got that factorisation yourself I was wondering if I could verify it for myself and quickly failed .

Thanks

For writing LaTeX what you really want is a text editor. Codecogs is very handy, but less good if you want to write whole documents in TeX and it does not have full functionality. What you shall need to do is download a LaTeX package, which should contain the LaTeX libraries and some software - if you're on windows I suggest MiKTeX, if you're on mac I suggest MacTeX - as for Linux, I'm not actually sure. These will come with editors which will probably suffice. MacTeX comes with TeXShop and MiKTeX has another, similar editor. As I say, these will do, but if you're serious about writing LaTeX then I highly recommend Vim (MacVim on Mac, gVim on Windows) or emacs, but please note that these take a small amount of setting up and are also designed such that it is possible to use them without ever touching your mouse. Use of the mouse is definitely possible, but ultimately they can take some getting used to. This would certainly be my advice, but in theory most text editors should be able to render LaTeX - as long as you have the LaTeX libraries installed. The thing with TeX is that it's a mark-up language, and hence you can't just open up a program and start entering it, you have to use a text editor to enter your text with mark-up (the LaTeX) and then a rendering engine to convert that into a nice output, which you can then view and print from in a pdf viewer. So you will need the libraries to render it, also, when writing LaTeX from scratch you will need a preamble - this declares certain packages and it is in line with these that your TeX is read and an output produced. You can't just type LaTeX all by itself, like you can on mathisfun (with the required delimiters, that is). I recommend you have a look at this http://en.wikibooks.org/wiki/LaTeX. There is also a pdf version and a link to it on the side of this webpage. It is a highly comprehensive manual and can teach you about most things - but I wouldn't advise reading the whole thing from start-to-finish, just look up what you need, when you need it. You should, however, read the first few pages to give yourself an understanding of what LaTeX is all about. But anyway, as I was saying, I would suggest those editors, but I believe you can theoretically use any text editor - even Microsoft's Notepad - but please, if you value your sanity - don't .

Hmmm, no I have reproduced the question in full and there is a worked solution which specifically says:

I assumed that I'd either completely misunderstood the question, or it was wrong. It's just that I'm used to seeing misprints in answer books, but an entirely illogical worked solution is something I wanted to check was the solution's mistake and not mine.