Analytic Implementation of Laplace Transform Algorithms Using the Digital Computer

The Laplace transform of a function can be recognized as the result of a finite number of operations perforned on the transform of a simple function. The rules governing the permissible sequences of operation have been established previously. The resultant algorithms have been used to teach Laplace transform techniques and have been applied in the derivation of transforms. From these algorithms a computer program has been developed to transform analytically from the t to the s domain. A brief survey of the algorithms is followed by a description of the program logic and grammar. Examples are given to illustrate the capabilities and limitations of the program. Possible applications and extensions of the program are discussed

Algorithm · Domain (mathematical analysis) · Fourier transform · Fractional Fourier transform · Function (biology) · Green's function for the three-variable Laplace equation · Inverse Laplace transform · Laplace transform · Laplace transform applied to differential equations · Laplace–Stieltjes transform · Mathematical analysis · Mathematical optimization · Mellin transform · Operational calculus · Post's inversion formula · Two-sided Laplace transform · Computer Science · Experimental Learning in Engineering · Mathematics