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Introduction to Differential 2 Forms  Math Berkeley

Introduction to Differential 2 Forms Math Berkeley

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this is the beginning of a series of videos where we're going to explore the notion of a differential form and so the goal is to look at a generalized version that Stokes theorem in the end okay so let's start off with a little definition so let's suppose that C is a curve in R 2 and P is a point on that curve so what we want to define is the tangent space to see at P and we will denote that by TPC so that's the set of all vectors that are tangent to see at P so I've drawn a little picture here so we can think about this is our plane R 2 and notice we have this yellow curve here I've put a point P on the curve and then my tangent space is really this tangent line although elements of this tangent space are vectors either pointing up in this direction of the line or down in that direction of the line and so the line that I've written is really the span of all of those vectors ok good so let's rephrase a simple question for

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