Discrete form of electromagnetic integral equations based on boxcar basis functions

4-3 Discrete form of electromagnetic integral equations based on boxcar basis functions 

We can select the basis functions in expansion (9.181) in the form of the boxcar functions multiplied by the values of the vector E (r ) at some internal point of the cell r G  

In this case, the scalar coefficients of the expansion (9.181) arc equal to 

According to a mean value theorem for integrals of the continuous functions, there is a mean vahie point r G for which 

We assume now that all points r coincide with the corresponding mean value points, r = r . In this case formula (9.187) for expansion coefficients takes the form 

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