Official TSR Mathematical Society

You do not require 'anything additional', this is more than approachable with the material you appear to have net.

Anyone know of notation for integrals over all space?
I'm getting bored of writing the infinity symbol up to 6 times per line so I've been using this notation in my notes:


But does anyone know of a better notation, if there is a standard notation for this?

If you're using known spatial co-ordinates (say $\mathbf{x} = (x,y,z)$) then we've been told we can write:

$\iiint_{\mathbf{x}} dS$

Don't know whether that's a just-one-lecturer thing though, as he's taken most of my Applied lectures.

Would that not require an additional $\forall (x,y,z)$, so $\mathbf{x} = (x,y,z) \forall (x,y,z)$ for additional clarity?
Though I guess that is quite concise. Cheers.

I guess if you state it once at the start it wouldn't hurt - then you can let it follow on from there.

Interesting way to denote all triples of real numbers: $\mathbb{R}^3$.

I think it is possible to abbreviate it as follows.

$\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} f(x,y,z)\ dxdydz$ can be the same as $\int_{\mathbb{R}^3} f(x,y,z)\ dV$.

In general, it can be $\int_{\mathbb{R}^n} f(\mathbf{x})\ d\mathbf{x}$, where $\mathbf{x} \in \mathbb{R}^n$ and $d\mathbf{x}$ is the corresponding n-dimensional differential.

At least, that's what the literature says.

EDIT: I like the infinity symbol in between them though.

Can somebody help me with this quesiton please:

cos3x = 4cos^2x

Meant to solve for 0 < x < 2pi

I know that cos3x = 4cos^3x-3cosx, so at first I rearranged and got:

4cos^3x - 4cos^2x -3cox = 0, then I divided everything by cosx ( which I'm not sure I'm actually meant to do), then factorised and got x=3/2 and x=-1/2

I'm pretty sure I've used the wrong method though, so could somebody point me in the right direction please?

Sorry about the untidiness aswell, I don't know how to actually write out the equation like I see you lot do in this thread

Thanks in advance

anyone doing/done a maths degree?,
I love maths; but the job prospects are anti-me finance, banking accounting is this true or just the majority of people go in to this field; how can I help people with a maths degree, I wan't a challenging job, maybe work in NASA I mean maths was involved for 'man landing on moon'

HELP.

Generally speaking NASA would recruit physicists for that kind of thing. The maths involved in a physics degree is more appropriate for space exploration than the maths in a physics degree. I guess the difference is that maths is more about proving statements, whereas physics simple accepts they are true and uses them to solve problems. At least that's my impression from speaking with mathematics students and from studying physics myself.

okay you've addressed the NASA issue, but what about job prospects that is the BIG issue here?

okay you've addressed the NASA issue, but what about job prospects that is the BIG issue here?

If you'd want to work in NASA or anything, I suspect you'd have to be quite good(and work on stuff like fluid dynamics or w/e).

apart from finance, banking and accounting what else could I do, anything related to computers?

The following is another nice question.


[*] For a positive integer $n$, compute the integral

$\displaystyle \int \frac{x^n}{1 + x + \frac{x^2}{2!} + \cdots + \frac{x^n}{n!}}\ dx$

A nice approachable question