Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

Pages: 1

#1 Re: Help Me ! » Proof of [AB,C]=A[B,C]+[A,C]B? » 2008-10-27 22:08:53

Talvon

Thanks for that, I can follow the proof but I'm unsure where A[B,C] and [A,C]B initially come from. Is it from the initial expansion, ie:

Does [AB, C] = ABC - CAB equal the same as [AB, C] = A[B,C] - [C,A]B?

Also, is a substitution made for [A,C]B in that it initially starts as [C,A]B but [C,A]= -[A,C]? It would explain the addition of the 2 rather than the subtraction tongue

Thanks again smile

Edit:

Never mind I read it wrong, I missed the point of adding in the (ACB-ACB) bracket, so doing it again with that in mind and re-arranging it it worked out :

So its ok to just put the factor of (ACB-ACB) in there, as it would just cancel itself without the re-arrangement anyway?

Cheers big_smile

#2 Help Me ! » Proof of [AB,C]=A[B,C]+[A,C]B? » 2008-10-27 08:53:25

Talvon
Replies: 3

I have to prove the theory above, the problem is I am a physics student and I am only aware that this is an application of ring theory and is Leibniz algebra by chance from another forum researching this problem, and so far I haven't been able to find a proof.

I tried it using twists on the commutator rule from quantum mechanics ([A,B]=AB-BA - I don't know how to handle commutators with powers in them neutral), and I got:

Q²R-RQ² => QR[Q]-[Q]

Which isn't working <_<

Any pointers would be greatly appreciated, as I haven't studied ring theory and it isn't part of my syllabus, so I don't know where to start tongue

#3 Re: Help Me ! » sinusoidal wave speeds???? » 2007-03-10 06:12:57

Talvon

omega=2pi*f (Omega=40 from your wave equation)

k (Wave number) = 0.2 - Again, lifted from wave equation

k=2pi/lambda

Use your values calculated and stick it in v=f*lambda smile

#4 Re: Help Me ! » I Need Help Bad!!! » 2007-03-07 03:29:13

Talvon

An old one I got told was

Silly Old Hitler (SOH) Couldn't Advance His (CAH) Troops Over America (TOA)

Kind of outdated and there's better ones out there

#5 Re: Help Me ! » Using Polar Coordinates to evaluate a double integral » 2007-03-07 03:18:35

Talvon

Excellent, I got it done tongue

Thanks a lot smile

#6 Re: Help Me ! » Using Polar Coordinates to evaluate a double integral » 2007-03-05 08:57:09

Talvon

I'm sorry but I don't get how -x² can equal -y² (From the page in your forum, which will be useful for the 2nd part of the question tongue Half the range of the integral = Half the solution <_<) (http://z8.invisionfree.com/DYK/index.php?showtopic=136)

I can reproduce it to the stage of rexp(-r²), and I am having trouble getting to the next part (-1/2exp(-r²)). I have tried integration by parts, using u=exp(-r²) and dv/dr=r, but it's coming out nowhere near what it should be. What should I use? Is this the correct method?

Also, would I be correct in writing:

π      ∞
∫ dθ ∫rexp(-r²) dr?
0     0

Thanks smile

#7 Help Me ! » Using Polar Coordinates to evaluate a double integral » 2007-03-03 12:23:48

Talvon
Replies: 5

I have this problem to do, and I've tried subbing in x=rcos and y=rsin, but I can't get it to do anything sad Any tips on how to get the ball rolling?

The problem is:

Use polar coordinates to evaluate
infinity
   ∫∫exp(-x²-y²)dydx
    0
and hence show that
  infinity
     ∫exp(-x²)dx=(√pi)/2
    0

Thanks

#8 Re: Help Me ! » Am i correct ? » 2006-12-12 10:18:13

Talvon

I did 4300/86 (As the other 86% of the group are employed), and then *100 to get the amount of people in the group as a whole (5000), then subtracted the employed people (4300) to get the remaining number of people on welfare in the group as 700.

Hope that may be useful tongue

#9 Re: Help Me ! » Integral evaluation question » 2006-12-12 09:10:36

Talvon

I got to ∫ cosh²(u) / sinh(u) dx, now I'm stuck again lol sad

Any tips? It's all in terms of u but with respect to x >_<

#10 Help Me ! » Integral evaluation question » 2006-12-11 00:46:19

Talvon
Replies: 7

It says 'evaluate from 0 to pi/4, the integral of e^x cos(2x) dx correct to 3sf'. I reckon it's an integration by parts, but I don't see how it is needed as both numbers give a value for when x=0. Any thoughts?

There's also another question that I don't understand on a similar topic, use the substitution x=sech(u) to evaluate the integral dx/(x(root of 1-x²)), don't know where to begin tongue

#11 Re: Help Me ! » Checking for vectors being linearly independant » 2006-11-22 05:07:04

Talvon

Awesome, thanks a lot big_smile

#12 Help Me ! » Checking for vectors being linearly independant » 2006-11-22 01:51:29

Talvon
Replies: 2

To check if a set of vectors are independent, do you just try and make a line equation out of them and it if doesn't work they are all independent of each other?

#13 Re: Help Me ! » Expansion of sec²x - Stuck :( » 2006-11-17 01:42:21

Talvon

A bunch of us got it in the end, we differentiated the tan x expansion to get the answer, if it's right or not we'll see on monday. So just so you know lol tongue

#14 Re: Help Me ! » Expansion of sec²x - Stuck :( » 2006-11-15 07:36:13

Talvon

Cheers but I think I'm meant to derive it from a list of standard expansions that I already have, and I figured the best one to use would be the cos expansion and invert it for the sec=1/cos thing, but I tried that and ended up getting it wrong sad I have others, like the expansion of sin x and 1/1+-x, etc.

Don't think I'm meant to do the differentiating and stuff myself.

Would sec²x= (1/cosx)(1/cosx)?

#15 Re: Help Me ! » chosen » 2006-11-15 04:47:43

Talvon

What about 235, 236 etc and all other combinations?

Sorry I don't know the formulas, I never did stats, something to think about tongue

#16 Help Me ! » Expansion of sec²x - Stuck :( » 2006-11-15 04:45:43

Talvon
Replies: 8

I have to show sec²x is approximately 1 + x^2 + 2x^4/3 + 17x^6/45

Anything x^8 and above is negligible.

I have looked at the standard expansions on the site, however, I have not yet studied the En number, so I won't be able to get away with it like that tongue

I tried using the identity that sec²x=1/cos²x, and using the standard Maclaurin expansion of cos (1-x²/2+x^4/4!-x^6/6!+...) and just squared it out but I got nowhere sad

Any help would be appreciated smile

Pages: 1

Board footer

Powered by FluxBB