1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

FLuxions. differenntials and power series

  1. Apr 5, 2010 #1
    1. The problem statement, all variables and given/known data

    The firstthing I need to note is this is for a HISTORY of math course, so we have to use non modern techniques in most cases, some not. In other words, thequestion describes how to solve them. I'm also on a compyuter with a terrible keyboard so I'm doing my best.

    Derive the power series for the logarithm by beginning with dy=1/(x+1)dx and assuming that y is apowerseries in x with undetermined coeeficients, and solving simple equations to determine each coeefficient in turn.

    2)solve the fluxonial equation x*/y*=2/x+3-x^2 by replacing x with x+1 and then using power series techniques

    NOTE: x* and y* are simply x with a dot above it, indicting derivtive of x in the old notation

    2. Relevant equations

    1) 1/(x+1)=1-x+x^2-x^3+....

    3. The attempt at a solution

    1) Well I know that if i intergate this i get the corretc solution, but they didnt have our modern integrating notations at the time. (this is Leibniz) and it syas to determine coofeicients, so I have no idea where to start

    2) i had no idea what to do here. I repce x with x+1 and got 2/(x+1) (whihc is 2 times the same expandion in 1) ) +3-(x^2+2x+1)

    No idea wht to do after that, I don't even know what I'm suposed to solve for.

  2. jcsd
  3. Apr 5, 2010 #2
    on problem 1)

    I said that y=a+bx+cx^2+dx^3....

    that is, y is some power series of x,

    then i took the derivative of that getting

    dy/dx =b+2cx+3dx^2....

    and let that equal the power series for 1/(x+1)

    that is,


    and get that b=1 2c=-1, this c=-1/2, and by the same logic d=1/3, e=1/4 etc etc.

    Would that be correct?
    Last edited: Apr 5, 2010
  4. Apr 5, 2010 #3
    for number 2, i thought about it more, and I'm thinking I need to solve to x*/y* in terms of a simple equation (like how 1-x+x^2-x^3+.... becomes 1/(x+1)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - FLuxions differenntials power Date
Powers of Prime Ideals Feb 22, 2018
Coefficient Matching for different series Jan 8, 2018
Integration of even powers of sine and cosine Nov 7, 2017