Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

Appendix F 287
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Notes:
• Since L −1 [ ()] recovers the original function (), the pair of functions ()
and () is said to form a Laplace pair.
• ThepropertiesoftheLaplaceandinverseLaplacetransformscanbederivedfrom
those of Fourier transforms (Zachmann 1972).
• Laplace transforms can be computed using symbolic algebra computer programs
(Maple, Mathematica, etc.). In favorable cases, it is also possible to obtain inverse
Laplace transforms by computer programs. However, it is often more convenient
to take the Laplace and inverse Laplace transforms from corresponding Tables. 57
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Table E.1: Table of Laplace transforms.
() () =L [ ()] () () =L [ ()]
()
()
() = R ∞
0
() −
() − ( =0) 1
−
1
1
1
( − ) 2
1
2
sin
2 + 2
2 2
1
3
cos
2 + 2
−1
Γ ()
1
1 ¡
− ¢ 1
( − )
( − )( − )
Γ () is the Gamma function. For integer , Γ () =( − 1)! (see Appendix F).
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References:
Houston 1996 P. L. Houston, Chemical Kinetics and Reaction Dynamics, McGraw-
Hill, Boston, 2001.
Steinfeld 1989 J. I. Steinfeld, J. S. Francisco, W. L. Haase, Chemical Kinetics and
Dynamics, Prentice Hall, Englewood Cliffs, 1989.
Zachmann 1972 H. G. Zachmann, Mathematik für Chemiker, Verlag Chemie, Weinheim,
1972.
57 Extensive Tables of Laplace transforms are given by (Steinfeld 1989).