Computing Kinetic Parameters Using Non-Linear Approximation Tools

3 Computing Kinetic Parameters Using Non-Linear Approximation Tools 

If akinetic curve equation is described by some analytical expression that cannot be transformed into a linear form, than the kinetic parameters of this equation can be found using a genf it function of Mathcad. 

This function should be discussed in detail. First, it has proven itself as a valuable and powerful tool starting from the early versions of Mathcad (interestingly enough, such a versatile suite as Maple did not have similar function for non-linear approximation, at least until the Maple 10 version). Additionally, the genf it function has changed a lot with the release of Mathcad 13. 

It is also known that the initial concentration of the compound A was Cao = 0.241 M. 

Mathcad 11 has successfully solved the problem as can be seen from comparison of the experimental data with the calculated kinetic curve. However, application of genf it required rather intensive preliminary work, since it was necessary to find the analytical expressions for partial derivatives of the function (4.16). Only two parameters are searched in this case and it required quite bulky constructions to be created. In Mathcad 12 and older versions, a user had to explicitly define a function vector containing the approximation expression as well as its partial derivatives on the approximation parameters. Additionally, this function had to have two arguments the first one being the independent variable, and the second one being the vector of sought parameters. However, the main inconvenience was in the fact that if the approximation function f (t, z) was defined according to 

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