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On QUADRATIC DIFFERENTIAL FORMS 1 Introduction in the Homes Esat Kuleuven

On QUADRATIC DIFFERENTIAL FORMS 1 Introduction in the Homes Esat Kuleuven

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[Music] we have a vector field F which is given by F of XY is x^2 + y cub in the I Direction + 2 sin x - y in the jth direction we want to compute the exterior derivative of the one form Associated to F let's recall that if we have a vector field F of XY which is given by P of XY in the I Direction plus Q of XY in the J Direction then the one form Associated to F is given by Omega F which is just P of XY DX plus Q of XY Dy this allows us to associate to any Vector field a one form and similarly to any one form a vector field so this defines a one form and I can compute the exterior derivative recall that that's just given by Computing the X partial derivative and then adding a DX X and then the Y partial derivative and adding a Dy this is exactly what we see when we use implicit differentiation and now what we have to do is wedge with DX and similarly if we differentiate uh 2 sin x - y with respect to X then what we get is 2 cine x - y DX and if we differentiate with re

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