## Integration of differential 1-forms. Differential k-forms and their integration

Integration of a 1-form over a smooth curve: use pull-back or approximate by the Riemann sums? Independence of the parameterization.

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Integral of along a smooth closed curve: area bounded by the curve.

Multilinear forms on a linear n-space. Tensor product.

Symmetric and antisymmetric multilinear forms. Symmetrization and alternation. Determinant. Wedge product. Algebraic properties of the wedge product, action by adjoint operators.

Differential k-forms and their integration along smooth k-dimensional “pieces” (images of a cube).