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Basic Complex Analysis Marsden Solutions PDF Form

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hello students in this video we'll see how to approach solving the LaPlace equation by using the same method as we did to solve the wave equation so if we recall if we had f t t was equal to c squared f x x then the general solution to this would be f of x t is going to be some function a of what a of X plus c t plus a function B of x minus CT that was the General solution to the one-dimensional wave equation we can actually plug this back in to check now we want to do is want to solve the LaPlace equation so the LaPlace equation I'm going to use x's and y's now this is more typical says that f X X Plus f y y is equal to zero so we're going to do is we're going to write this as fyy fyy is equal to negative f x x and then what I'm going to do is I'm going to take negative negative 1 and I'm going to write as I squared so this is f y y is equal to I squared f x x and so we see from this we can say at least formally i

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