Vector calculus

• What Is a Divergence-Free Vector Field?
  Learn how to identify divergence-free vector fields, interpret zero divergence, construct examples, and use the divergence theorem to calculate flux.
• How to Calculate Divergence in Curvilinear Coordinates
  Derive the divergence formula in curvilinear coordinates, then apply it to cylindrical and spherical vector fields with worked examples.
• How Are the Dot Product and Divergence Related?
  The divergence of a vector field is written as nabla dot F: take each component's matching partial derivative and add the results.
• What Is the Coordinate-Free Definition of the Nabla Operator?
  Nabla is not one universal coordinate-free vector: the gradient comes from a metric, while covariant differentiation comes from a connection.