Introduction to error estimation

One of the most difficult tasks in day-to-day scientific activity is making reliable estimates of the errors and uncertainties in the data. How reliable are my data How accurate are the parameters calculated from them Can I, or should I, exclude particular models for explaining my data These are examples of the sort of questions that need to be asked. We have already discussed the question of judging how well 

Kinetic processes can be described by differential equations for example, for a reversible bimolecular assodation reaction  

This equation defines directly the change in concentration of the spedes AB with given concentrations of the reactants A and B, and the product AB. This is a differential equation whose solution is an expression of the form cAB=f(t, c% eg). The solution involves a process of integration, which is often difficult, and sometimes impossible, at least analytically. In such cases, numerical integration can be used to simulate the time-dependent variation of cAB in an experiment, enabling theoretical data to be obtained even for complex systems. 

The procedure for numerical integration is as follows. Initial conditions are first selected cA, cB, cAB and from this initial state the concentrations of the three component species are altered stepwise using fluxes defined from the differential equation given above, with a finite time increment At. 

The concentration changes are defined in terms of these fluxes as follows  

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