This Appendix contains 196 common Laplace transforms which are frequently encountered in applied mathematics. The familiar reader will note that the indexing method differs somewhat from the usual method. In this table we have introduced an index notation which hopefully will provide a more efficient means of using the tables to find a desired transform pair. The basic transforms have been cataloged by the standard numerical method where the numerical value denotes the order of the denominator of g(s). For the more complex forms an alphabetic index has been used which is described in Table 1. The references at the end of Table 2 cite other works which contain extensive tables of Laplace transforms.
Table 1 Summary of index notation employed in cataloging transforms
Table 2 Laplace-transform pairs
1954. A. Erdélyi (ed.): “Tables of Integral Transforms,” vol. I, McGraw-Hill Book Company, New York.
1963. Ryshik, I. M., and I. S. Gradstein: “Tables of Series, Products, and Integrals,” VEB Deutscher Verlag Der Wissenschaften, Berlin, p. 249 ff.
1965. Fodor, G.: “Laplace Transforms in Engineering,” Akademiai Kiado, Budapest, p. 691 ff.
1965. McCollum, P. A., and B. F. Brown: “Laplace Transform Tables and Theorems,” Holt, Rinehart and Winston, Inc., New York.
1966. Roberts, G. E., and H. Kaufman: “Table of Laplace Transforms,” W. B. Saunders Company, Philadelphia.
† X denotes a numerical value.