To find the Laplace transform of L using the definition of the Laplace transform, we’ll need to multiply f(t) by e^(-st), then integrate that product on the interval [0,infinity). This is the definition of the Laplace transform, such that the result is the Laplace transform of f(t), which we write as F(s).
Read MoreNormally when we do a Laplace transform, we start with a function f(t) and we want to transform it into a function F(s). As you might expect, an inverse Laplace transform is the opposite process, in which we start with F(s) and put it back to f(t).
Read MoreTo use a Laplace transform to solve a second-order nonhomogeneous differential equations initial value problem, we’ll need to use a table of Laplace transforms or the definition of the Laplace transform to put the differential equation in terms of Y(s). Once we solve the resulting equation for Y(s), we’ll want to simplify it until we recognize that the terms in our equation match formulas in a table of Laplace transforms.
Read MoreTo find the Laplace transform of a function using a table of Laplace transforms, you’ll need to break the function apart into smaller functions that have matches in your table.
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