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Combining three non linear functions into one single function

  1. Aug 10, 2010 #1
    combining three non linear functions into one single function....

    I am performing one experiment in which I have a system output as Q which fundamentally depends on 3 independent inputs h,P,F.
    i.e. Q=G(h,P,F)....where G is some function.
    To quantify the dependence I varied h keeping P,F constant and got a variation in Q.

    Similarly I got another experimental plot of Q vs P where h,F are constant
    and also one Q vs F plot for constant h,P
    I did a curve fit in MATLAB cftool and obtained some non linear functions.
    The equations are of the following form
    Q=a1*ln(h)+b1.....P,F constant
    Q=a2*P^b2+c2....h,F are constant....^ denotes exponentiation.
    Q=a3*F^b3+c3....h,P are constant , ^ denotes exponentiation.
    a1,a2,a3,b1,b2,b3,c2,c3 are all known constants.
    what I want is to combine these three functions of h,P,F and obtain G such that Q=G(h,P,F)
    any help?
  2. jcsd
  3. Aug 10, 2010 #2


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    Re: combining three non linear functions into one single function....

    Taylor series approach might be fruitful. Since you have equations for the 1st partial derivatives of Q with respect to each of the three variables, you can calculate higher order partial derivatives.
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