Combining three non linear functions into one single function

In summary: Then you can use Taylor series to approximate G(h,P,F) around any point (h0,P0,F0) as a polynomial of h-h0, P-P0, F-F0.In summary, the conversation discusses the process of combining three non-linear functions into one single function, represented as Q=G(h,P,F). The three independent inputs, h, P, and F, are varied to quantify the dependence on each input. The result is three experimental plots of Q, each with two of the inputs held constant. By performing a curve fit in MATLAB, non-linear functions are obtained for each plot. The goal is to combine these functions into one overall function, G, and the Taylor series approach is suggested as a possible method
  • #1
souviktor
7
0
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?
 
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  • #2


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.
 

1. How do you combine three non-linear functions into one single function?

To combine three non-linear functions into one single function, you simply need to substitute each function into the other. For example, if you have three functions f(x), g(x), and h(x), you would write a new function with the form f(g(h(x))). This will combine the three functions into one.

2. Can you combine non-linear functions if they have different variables?

Yes, you can still combine non-linear functions if they have different variables. You just need to make sure that the variables are consistent throughout the equations. For example, if one function has the variable x and another has the variable y, you can rewrite one of the functions in terms of the other variable before combining them.

3. What are the benefits of combining non-linear functions into one single function?

Combining non-linear functions can make it easier to analyze and understand the behavior of the functions. It can also help in solving complex equations and finding a single solution. Additionally, it can also save time and space by reducing the number of equations needed to represent the functions.

4. Are there any limitations to combining non-linear functions into one single function?

Yes, there are some limitations to combining non-linear functions into one single function. For example, the functions must be compatible and have a common domain and range. Additionally, some combinations may result in a function that is not continuous or differentiable, making it difficult to use in certain applications.

5. Can you combine more than three non-linear functions into one single function?

Yes, you can combine more than three non-linear functions into one single function. The process is the same as combining three functions, where you simply substitute one function into the other until you have a single function. However, as the number of functions increases, the complexity of the resulting function may also increase.

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