Examples of using The laplace transform in English and their translations into Hebrew
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But the Laplace Transform it is an integral.
And I have gotten a bunch of letters on the Laplace Transform.
The Laplace transform of this is equal to this.
And we showed that the Laplace transform is a linear operator.
The Laplace Transform got us something useful.
People also translate
Because you will actually solve something with the Laplace Transform.
So the Laplace transform of this is equal to that.
Well let me factor out the Laplace Transform of y part.
The Laplace Transform, the notation is the I like Laverne from Laverne and Shirley.
I will now introduce you to the concept of the Laplace Transform.
And remember, the Laplace transform is just a definition.
I'm going to say the Laplace Transform of y is equal to something.
And I think where I left, I said that I woulddo a non-homogenous linear equation using the Laplace Transform.
This was the definition of the Laplace transform of sine of at.
So the Laplace transform, and I will just say that's y, y is equal to-- y is what we're trying to solve for, the.
A function is equal to two times the Laplace transform of that function and vice versa.
So the Laplace transform of e to the t cosine of t became s minus 1 over s minus 1 squared plus 1.
Because if a is equal to 0, then the Laplace transform of e to the 0 is just 1/s minus 0.
The Laplace transform of t squared is equal to 2/s times the Laplace transform of t, of just t to the 1, right?
Let me put the Laplace transform of-- and I'm also going to the sides.
The Laplace transform of any function is equal to the integral from 0 to infinity of that function times e to the minus st, dt.
Our definition of the Laplace transform, that says that it's the improper integral.
So the Laplace transform of some function of t is equal to the improper integral from 0 to infinity of e to the minus st times our function.
Whatever my exponent is, the Laplace transform has an s in the denominator with one larger exponent.
Then if you take the Laplace transform of that, that means that F of s is equal to s minus 1 over s minus 1 squared plus 1.
And notice, using the Laplace Transform, we didn't have to guess at a general solution or anything like that.
We can now figure out the Laplace transform of a higher power in terms of the one power lower that, but it still doesn't give me a generalized formula.