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taylor expansion

Discussion in 'Members' Lounge' started by pills_PMD, Mar 3, 2006.

  1. pills_PMD

    pills_PMD Super Moderator

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    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)
     
  2. Capt. Orygun

    Capt. Orygun Win the Day

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    The awnser is 4 :p
     
  3. pills_PMD

    pills_PMD Super Moderator

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    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
     
  4. Capt. Orygun

    Capt. Orygun Win the Day

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    wait a second, I was right?
     
  5. pills_PMD

    pills_PMD Super Moderator

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    lol. no... but close
     
  6. Slammed90Lude

    Slammed90Lude Senior Member

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    who the hell does taylor series expansions for fun? :p
     
  7. pills_PMD

    pills_PMD Super Moderator

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    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
     
  8. MugenCRX

    MugenCRX Senior Member

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

    Capt. Orygun Win the Day

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    fuck that I jut guessed lol

    what is that used for?
     
  10. dveit

    dveit Well-Known Member VIP

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

    Capt. Orygun Win the Day

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

    EGProject YEEEEAAHHHHH

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    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.... [​IMG]
     
  13. pills_PMD

    pills_PMD Super Moderator

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    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
     
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