Dr. Robert Lopez

Essentials of Tensor Calculus - Part 2

In the second installment of the Essentials of Tensor Calculus series, Dr. Robert Lopez will explain reciprocal vectors and show that bases of tangents and gradients are reciprocal. This is important because these distinctions underpin the difference between contravariance and covariance. The transition matrix for a natural basis of tangent vectors or gradient vectors will turn out to be a Jacobian matrix. The contravariant and covariant transformation laws arise from these explorations.
Language: English
Duration: 42 Minutes
Related Terms: Tensor, Calculus, Reciprocal, Tangent, Gradient, Covariance, Jacobian