As of Version 9.0, vector analysis functionality is built into the Wolfram Language

Coordinate Systems

 

ReferenceReference

Cartesian Cartesian coordinate system

Cylindrical cylindrical coordinate system

Spherical spherical coordinate system

Paraboloidal  ▪  ParabolicCylindrical  ▪  EllipticCylindrical  ▪  ProlateSpheroidal  ▪  OblateSpheroidal

Bipolar bipolar coordinate system

Bispherical bispherical coordinate system

Toroidal toroidal coordinate system

Conical  ▪  ConfocalEllipsoidal  ▪  ConfocalParaboloidal