Laplace transform explain please don't spam anyway I will reporting your I'd
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In mathematics, the Laplace transform, named after its inventor Pierre-Simon Laplace, is an integral transform that converts a function of a real variable to a function of a complex variable. The transform has many applications in science and engineering because it is a tool for solving differential equations.
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c \displaystyle G\left( s \right) = \frac{{3s - 2}}{{2{s^2} - 6s - 2}} Show Solution
d \displaystyle H\left( s \right) = \frac{{s + 7}}{{{s^2} - 3s - 10}} Show Solution
The last part of this example needed partial fractions to get the inverse transform. When we finally get back to differential equations and we start using Laplace transforms to solve them, you will quickly come to understand that partial fractions are a fact of life in these problems. Almost every problem will require partial fractions to one degree or another.
Note that we could have done the last part of this example as we had done the previous two parts. If we had we would have gotten hyperbolic functions. However, recalling the definition of the hyperbolic functions we could have written the result in the form we got from the way we worked our problem. However, most students have a better feel for exponentials than they do for hyperbolic functions and so it’s usually best to just use partial fractions and get the answer in terms of exponentials. It may be a little more work, but it will give a nicer (and easier to work with) form of the answer.
Be warned that in my class I’ve got a rule that if the denominator can be factored with integer coefficients then it must be.
So, let’s remind you how to get the correct partial fraction decomposition. The first step is to factor the denominator as much as possible. Then for each term in the denominator we will use the following table to get a term or terms for our partial fraction decomposition.