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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 equa
by 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 agoSorry, 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 agoThat'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 agoOne 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 agoThat'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).