Rating is available when the video has been rented.
This feature is not available right now. Please try again later.
Uploaded on May 20, 2009
A brief look at applications of differential geometry and the concept of contravariant and covariant components of a vector. It is shown that in the simple case of an oblique coordinate system in two dimensional Euclidean space the formula for the length requires covariant and contravariant components of a vector. The metric tensor is introduced and its components found using coordinate transformation matrices. Mysterious upper and lower vector indices are explained. More sophisticated algebraic operator versions of this concept, including the tangent and co-tangent dual, will be discussed in future videos.