General partial fraction theorem

Forcing function, 143 periodic, 144 transient, 143 Fourier transform, 170 Fractional time, 29 Fractionation factor, 301 Fraction theorem, general partial, 85 Frame, rotating, 170 Franck-Condon principle, 435 Free energy, 211 transfer, 418... 

Applying the general partial fraction theorem, Eq. (3-72), to Eq. (3-96) and then taking inverse transforms gives Eq. (3-99). 

Benet, L.Z. Turi, J.S. Use of general partial fraction theorem for obtaining inverse laplace transforms in pharmacokinetic analysis. J. Pharm. Sci. 1971, 60, 1593-1594. 

We have derived the general Inversion theorem for pole singularities using Cauchy s Residue theory. This provides the fundamental basis (with a few exceptions, such as /s) for inverting Laplace transforms. However, the useful building blocks, along with a few practical observations, allow many functions to be inverted without undertaking the formality of the Residue theory. We shall discuss these practical, intuitive methods in the sections to follow. Two widely used practical approaches are (1) partial fractions, and (2) convolution. 

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