Courses

Binary space, Multilinear forms. Tensor product. Differential forms in ℝn. Exterior product. Exterior derivative. Closed and exact forms. Feeding representation. Hodge's * operator. The three fundamental theorems of vector analysis via differential forms. Application of differential forms to surface theory (Cartan's moving frame). Introduction to the integration of differential forms in ℝn. Derivative by direction in ℝn. Tangent vectors in R^n as derivatives. Vector fields in ℝn. Differentiable manifolds. Smooth mappings between manifolds. Tangent vectors as derivatives. Tangent space. The differential of a smooth mapping. Vector fields and 1-forms on manifolds. Information: Replaces the Course "Tensor Analysis and Geometry" from the Academic Year 2021-22.