Table Al 



Short Table of Laplace Transforms of Functions Often 



Encountered in Solving the Diffusion Equation 



y(s) 



y(t) 



-i x 



(fe) 



1/2 2,. . 

 -x /4et 



-q x 



erfc 



2/ET 



j-qx 



qs 



, M 1/2 -x 2 /4et 

 2 I ^— J e - x erfc 



(?) 



\2/ilj 



-q x 



1+1 /2n 



,.,l/2n .n _ 

 (4t) i erfc 



V2/FF/ 



n = 0, 1, 2. 



e~ qx 



q + h 



(fe) 



!/2 2 // . u u2 

 -x /4et , hx+eth 

 e - hee erfc 



2/et 



+ h/et 



qs 



e'^ 2/et\ 



(q + h) h \n ) 



1 /? ? 



-xV4et /l + hx 



erfc 



2/et 



, 1 hx+eth - / x , , r— 

 H =■ e erfc j + h/et 



h' \2/eT 



h is an unrestricted constant 



A3 



