Inverse Laplace transform, also known as inverse Laplace transform, is an integral transform commonly used in engineering mathematics. It exists in the following three situations: (1) pole is a real number without multiple roots; (2) The pole is the compound root of the yoke; (3) There are many real roots.

The first case of Laplace inverse transformation is that the poles are real numbers and there are no multiple roots. In this case, it is relatively simple to do the inverse transformation. Let's judge F(s) first. Whether it is a true fraction (the highest denominator is greater than the numerator), if not, first convert it into a true fraction. After determining that it is a true fraction, it can be simplified by factorization. The solution of the second case and the third case is relatively complicated.

Laplace inverse transformation formula

Laplace transform can transform a differential equation into an algebraic equation with complex variables, that is, a function of real number t(t≥ 0) into a function of complex number s, and the inverse Laplace transform is the process of solving the original image function f(t) from the image function F(s).

Laplace transform comparison table