Laplace transform is an integral transform commonly used in engineering mathematics, also known as Laplace transform. Engineering mathematics is the general name of several kinds of mathematics. After engineering students finish advanced mathematics in their freshman year. We should study integral transformation, complex variable function, linear algebra, probability theory, field theory and other mathematics according to our major, which belong to engineering mathematics. Mathematical physical equations and special functions are also a branch of engineering mathematics.

Laplace transform is widely used in many fields of engineering technology and scientific research.

If for the real part σ >; The above-mentioned integrals of S value of σc exist, but they do not exist when σ ≤σc, so σc is called the convergence coefficient of f(t). For a given real variable function f(t), Laplace transform F(s) only exists when σc is finite. Traditionally, F(s) is often called the image function of f(t), which is denoted as f (s) = l [f (t)]; Let f(t) be the original function of F(s), and let f(t)=L- 1[F(s)].

Laplace transform is suitable for continuous time function x(t) with t > = 0 with non-zero function value. By applying Laplace transform to solve homogeneous differential equations with constant variables, differential equations can be transformed into algebraic equations. In engineering, the great significance of Laplace transform lies in: transforming a signal from time domain to complex frequency domain (S domain) to represent it; It is widely used in linear systems and control automation.