Keyword: «laplace transform»

The paper considers a brief theoretical information related to the application of operational calculus. The authors tabulate originals and images, basic theorems and models for the location of the image for the original; describe the ways to restore the original according to the known image. Since the classical methods of solutions of the Cauchy problem for linear differential equations with constant coefficients and right-hand side in the form of a composite function are highly intensive, clearly shows the efficiency of application of operational calculus and solutions of such problems. The parsed solution of the Cauchy problem for the Duhamel formula.

This article proposes a version of presenting material on the subject “Laplace transform. Finding the image by the original” in a concise form. The main theorems are examined with the help of which images are found by originals and vice versa. Examples are chosen in such a way as to clearly illustrate each theorem and the basic concepts of the subject. The content of the article will serve as a material for the second year students’ classes preparation when they study the section “Operational Calculus” and will be useful to both teachers and students.