Nonlinear curve fitting

Lab for Nonlinear Curve Fitting
Module for Nonlinear Curve Fitting
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Background. The method of "linearization of the data" will is used.Exponential curve fitting
for the data points .
The method of "linearization of the data" will is used.

Take the logarithm of both sides: ln(y) = ln(c) + a x .

Introduce the change ofvariables: X = x and Y = ln(y).

The previous equation becomes Y = ln(c) + a X which is now "linearized."

Use this change of variables on all the data points:

i.e. same abscissa's but transformedordinates in this case.

Now you have transformed data points: .

Use the "Fit" procedure get Y = A X + B, which must match the form Y = ln(c) + a X so you see that and a = A.

First loadMathematica's graphics package "Colors".

 
 
 

Report to be handed in.
Computer Exercises 




 
 
 
 
Exercise 1. Fit the curve to the data points (0,1.5), (1, 2.5),(2, 3.5), (3, 5.0) and (4, 7.5).
Solution. Enter the point into a two dimensional array;

Look at the transpose of this "list of lists."


The twoportions of this data structure are separated by breaking off the first and second parts of the "list of lists" tr[[1]] and tr[[2]] .


We want to use the sameabscissas, and take the logarithm of the ordinates. Notice that Mathematica uses Log[x] for the natural logarithm ln[x] this is because it has been taught the proper notation used in "Complex Variables"i.e. the terminology Log[x] is used in advanced mathematics.


Now glue together the transformed parts to form the pairs .


Now...