Integral Transforms (Operational Calculus)

Abstract

For solving certain types of ordinary differential equations, particularly those with constant coefficients, and certain types of partial differential equations (e.g. equation of heat conduction, of string and diaphragm vibrations, etc.) in special domains, transform methods may be advantageously used. From among them, the Laplace-Carson transform is formally identical with the operational calculus, and the finite Fourier transform leads to the expansion of a function in a Fourier series.