To use the Laplace transform tables to find the Laplace transforms of modified basic functions such as scaling, sums and differences of functions, and functions multiplied by t and to use the tables of functional Laplace transforms and operational Laplace transforms to find the Laplace transform of a given function. The Laplace transform is a powerful tool for solving differential equations in mathematics, physics, and engineering: at its core, a Laplace transform turns a differential equation into an algebraic equation, the idea being that an algebraic equation is generally more easily solved than an arbitrary differential equation. Because the Laplace transform is used in so many disciplines, many of the most-common transforms have been calculated and can be found in tables so it is not necessary to compute the transforms from the integral definition every time. Although most of this tutorial can be done using only the tables, it is good practice to at least try to find the Laplace transforms of some of them by direct integration The feedback and hints will be of the most value to those students who do try the integration Scaling in the time dimension Find the Laplace transform of the function f(t) = 4t Give an exact answer in the s domain. The Laplace transform of sums and differences Find the Laplace transform of the function f(t) = t + e^-2.5t -cos3.2t. A Laplace transform involving a product with a linear function of time Using the Laplace transform tables or direct integration, find the Laplace transform of the function f(t) = (t 6.8)sin 6.2t.