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It should say Laplacian in OP's post, not Laplacian Transform (if I am not mistaken). The Laplacian is a matrix of (partial) derivitives and is used for the equ

It should say Laplacian in OP's post, not Laplacian Transform (if I am not mistaken). The Laplacian is a matrix of (partial) derivitives and is used for the equational conversion.

mkl 7y ago
It should be "Laplace transform". This video has nothing about Laplacians at all. Are you thinking of the Jacobian matrix? I'm not sure what you mean by equational conversion. The Laplacian matrix is from graph theory and doesn't involve derivatives. The Laplacian operator involves differentiation, but is not a matrix.
- mikorym 7y ago
  Sorry, sorry. You are right, I am thinking of the Jacobian. What does the comment mean then? > "Also, apparently the Laplacian Transform can be used to convert Calculus derivative equations into algebraic ones..."
  - mkl 7y ago
    That's the primary reason to use the Laplace transform, as seen in the video. A derivative x'(t) gets transformed into a product (and an initial condition), s X(s) - x(0), and similar for higher derivatives, so a differential equation transforms into an algebraic equation, which can be solved by rearranging. This video assumed the initial conditions like x(0) = 0, and its notation was quite sloppy/confusing in places, as it didn't clearly distinguish the names of the two functions, x(t) and X(s).
- mikorym 7y ago
  One more point to sort this out. Is Laplacian always that modified adjacency matrix in graph theory, or does it mean something else as well?
  - mkl 7y ago
    That's the "Laplacian matrix". "Laplacian" as a noun usually refers to the differential operator, and "Laplacian" as an adjective is attached to quite a few things as well as the natrix (mostly developed or worked on by Laplace, or based on such).
Jugurtha 7y ago
> It should say Laplacian in OP's post, not Laplacian Transform (if I am not mistaken). Neither. It's "Laplace Transform". > The Laplacian is a matrix of (partial) derivitives and is used for the equational conversion. Bar the name, this is called Operational Calculus[0]. [0]: https://en.wikipedia.org/wiki/Operational_calculus https://en.wikipedia.org/wiki/Operational_calculus

It should say Laplacian in OP's post, not Laplacian Transform (if I am not mistaken). The Laplacian is a matrix of (partial) derivitives and is used for the equational conversion.

mkl 7y ago

It should be "Laplace transform". This video has nothing about Laplacians at all. Are you thinking of the Jacobian matrix? I'm not sure what you mean by equational conversion. The Laplacian matrix is from graph theory and doesn't involve derivatives. The Laplacian operator involves differentiation, but is not a matrix.

mikorym 7y ago
Sorry, sorry. You are right, I am thinking of the Jacobian. What does the comment mean then? > "Also, apparently the Laplacian Transform can be used to convert Calculus derivative equations into algebraic ones..."
- mkl 7y ago
  That's the primary reason to use the Laplace transform, as seen in the video. A derivative x'(t) gets transformed into a product (and an initial condition), s X(s) - x(0), and similar for higher derivatives, so a differential equation transforms into an algebraic equation, which can be solved by rearranging. This video assumed the initial conditions like x(0) = 0, and its notation was quite sloppy/confusing in places, as it didn't clearly distinguish the names of the two functions, x(t) and X(s).
mikorym 7y ago
One more point to sort this out. Is Laplacian always that modified adjacency matrix in graph theory, or does it mean something else as well?
- mkl 7y ago
  That's the "Laplacian matrix". "Laplacian" as a noun usually refers to the differential operator, and "Laplacian" as an adjective is attached to quite a few things as well as the natrix (mostly developed or worked on by Laplace, or based on such).

Jugurtha 7y ago

> It should say Laplacian in OP's post, not Laplacian Transform (if I am not mistaken). Neither. It's "Laplace Transform". > The Laplacian is a matrix of (partial) derivitives and is used for the equational conversion. Bar the name, this is called Operational Calculus[0]. [0]: https://en.wikipedia.org/wiki/Operational_calculus https://en.wikipedia.org/wiki/Operational_calculus