Recent content by Zeth

I'm such a messy thinker that I've sworn off paper if at all possible for the simple reason that I run out of space all the time. On average, to have a readable semi-presentable piece of work, I would need three drafts made with pencil. Computers aren't much better, even though with a graphics...

"Let S be a set. The set F(S,R) of all functions f : S → R from S to R is a real vector space." The above means that F is a collection of all possible functions that take some value, real or imaginary (or worse), and return a real number?

Yes I noticed that gamma should be negative as well since it doesn't make sense for predators to grow exponentially even if they catch no prey. I'll ask the lecturer about it. And thanks I'm having a look at the wikipage for it now. "The way I'd do it, is to "linearize" the system of eqns...

Homework Statement \frac {dA} {dx} = \alpha A - \beta AB \frac {dB} {dx} = \gamma B + \delta AB Let A(x) and B(x) be two populations that influence each other and treat A(x) as a function of B, find an ODE for A(B). This is an extention revision problem so its not in my notes. What...

Homework Statement \int \!\sqrt {1+{v}^{2}}{dv} Homework Equations Maple tells me that I have to throw in an arcsinh into the solution some how. The Attempt at a Solution I've tried substituting with tan(x) but that got me no where and from the solution I'm given: 1/2\,v\sqrt...

Thanks a lot, that has just the properties I needed for the proof.

If you get paid for it you are. By which standard I'm a petroleum engineer, which just goes to show how misleading job titles can be. For general information I'm a first year math/physics student. The closest I've come to being a physicist is being mistaken for a lecturer last week. Something...

This is for a proof but I was generally more curious so it isn't in the homework section. If I were to make a set A which is defined as all the prime factors of an integer a there could be some numbers in A which are repeated, would these count as distinct members or not? The reason why I was...

So is my working is otherwise correct? I'm going out to an open seminar so I don't have time to learn and try what you suggested right now.

\int_{-2} ^2 \frac{dx}{4+x^2} I use the trig substitution and get everything done but for some reason I can't get the answer, here's all my working: x = 2 \tan\theta dx = 2 \sec^2\theta 4+x^2=4(1+\tan\theta)=4\sec^2\theta \int \frac{2\sec^2\theta d\theta}{4\sec^2\theta} \int...

Homework Statement \int_0 ^\pi \sqrt{1-\sin^2 x} dx Homework Equations 1 - \sin^2 x = \cos^2 x The Attempt at a Solution I don't know how to treat this since cos changes sign half way across the integral. I know the answer should be 2 but I keep getting 0 every which way I try.

This will make for an interesting thread: The teenage years of physicists. And you're not disadvatnaged if you're prepared to work to gain ground. In some ways you might even be in a better position learning the material later, you'll bring a more mature brain to bear against the ideas you'll be...

IQ measures how well you do in IQ tests, not to mention denoting a 3 hour period in your life which could have been better spent watching paint dry. As for genius it in the eye of the beholder rather than in the head of the beholdee.

lol I can't believe I missed that, sleep it is. Thanks a lot.

I'm probably wrong but I tried that and it doesn't seem to work: I end up with \int \frac{2\theta+1}{(\theta+1)^2+1} d\theta and u = \theta +1 du = d\theta but the top line still looks like 2\theta +1 best I've managed is: \int \frac {(2\theta +2)-1}{(\theta+1)^2+1} d\theta which I still...