2. The coefficients A and B are determined by the transformed 

 boundary conditions and are, in general, functions of the parameter s . To 

 obtain a solution in the time domain, Equation A4 has to be inverse trans- 

 formed. This can be accomplished using tables of known transforms (see, for 

 example, Erdelyi et al. (1954) and Abramowitz and Stegun (1965))* or the 

 Fourier inversion theorem which states 



5+1; 



" y(s) ds (A5) 



£~-io° 



5+lco 

 1 f st 



-3H J e 



The integration is performed as a line integral in the complex plane, for 

 which 5 is taken sufficiently large to have all singularities of the func- 

 tion y(s) lying to the left. Equation A5 is normally evaluated by means of 

 the residue calculus. If several solution areas are used, the solution within 

 each area is of the form of Equation A4 . The solutions are dependent upon 

 each other through their common boundaries (as an example see Appendix E) by 

 the prevailing boundary conditions. 



3. Table Al presents a short summary of selected applicable transforms 

 useful for solving the diffusion equation. 



* References cited in the Appendix can be found in the References at the end 

 of the main text. 



A2 



