taylor expansion

[pills_PMD]

if anyone knows what i am talking about say "I".

i'm looking for free energy interaction coefficients... trying to expand

gamma2(infinite)*x2*exp(J1(2)*x2+J2(2)x2^2+...+Ji(2)x2^i)


that's kind of hard to interpret, but i can scan in the equation if anyone might have a remote idea


and no this isn't asking for HW help... this is just for fun

forgot to add gamma2(infinite) is a constant.... expand about point(x2=0)

 

[Capt. Orygun]

The awnser is 4

 

[pills_PMD]

actually i figured it out...

keep gamma2(inf) and x2 out of the expansion

expand exp(x) as 1 + x + x^2/2 + x^3/6 + ....
put the Ji(n) terms in front of it.. multiply the x2 in multiply the gamma term in.. BAM!

thanks for the help

 

[Capt. Orygun]

wait a second, I was right?

 

[pills_PMD]

lol. no... but close

 

[Slammed90Lude]

who the hell does taylor series expansions for fun?

 

[pills_PMD]

i'm actually studying for a thermodynamcis final... i had diff eq like 3 years ago and haven't used any of it since... now every time i turn around it's like "taylor expand this..." "taylor expand that"
i can't wait until thermo is over

 

[MugenCRX]

You... my friend.... are very smart. Like my roommate who is majoring in AstroPhysics.

 

[Capt. Orygun]

fuck that I jut guessed lol

what is that used for?

 

[dveit]

I don't think he was talking about you. Pills.

 

[Capt. Orygun]

no shit einstein, I was just wondering what this was actually used for

 

[EGProject]

It's differential eqations - as he said before. A lot of fluid and thermodynamics stuff uses eqations and operations like that.


Oh, the work I look forward to....

 

[pills_PMD]

basically it tells you how a function approaches a point. it's an infinite series expansion that really has no end, but you can estimate the error depending on how many terms you "expand" it's a special type of power series, but it has many applications in thermodynamics, diffusion kinetics and a million others i'm sure.. but my major use is thermo/diffusion