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Moreover, a 2-form is a smooth choice of a skew-symmetric bilinear form on each of the tangent spaces of your manifold. A 2-form is non-degenerate if it is non-degenerate (as a bilinear form) when restricted to each tangent space. This aspect of What Is A Differential Form Mathematics Stack Exchange plays a vital role in practical applications.
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Furthermore, a differential form is a generalisation of the notion of a differential that is independent of the choice of coordinate system. An n-form is an object that can be integrated over an n-dimensional domain, and is the wedge product of n differential elements. This aspect of What Is A Differential Form Mathematics Stack Exchange plays a vital role in practical applications.
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Furthermore, the second equation is not elementary it is a statement about differential forms. As Mathematleta suggests, the definition of a differential form involves a lot of machinery, and is best learned over the course of a month or so. This aspect of What Is A Differential Form Mathematics Stack Exchange plays a vital role in practical applications.
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Furthermore, a differential form is a generalisation of the notion of a differential that is independent of the choice of coordinate system. An n-form is an object that can be integrated over an n-dimensional domain, and is the wedge product of n differential elements. This aspect of What Is A Differential Form Mathematics Stack Exchange plays a vital role in practical applications.
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Moreover, a differential form is a generalisation of the notion of a differential that is independent of the choice of coordinate system. An n-form is an object that can be integrated over an n-dimensional domain, and is the wedge product of n differential elements. This aspect of What Is A Differential Form Mathematics Stack Exchange plays a vital role in practical applications.
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