▁cyl ind rical ▁polar ▁coordinates ▁ ▁Hence , ▁ ▁Represent ing ▁a ▁physical ▁second - order ▁tensor ▁field ▁The ▁physical ▁components ▁of ▁a ▁second - order ▁tensor ▁field ▁are ▁those ▁obtained ▁when ▁the ▁tensor ▁is ▁expressed ▁in ▁terms ▁of ▁a ▁normal ized ▁cont rav ari ant ▁basis . ▁ ▁In ▁cyl ind rical ▁polar ▁coordinates ▁these ▁components ▁are ▁ ▁Grad ient ▁of ▁a ▁second - order ▁tensor ▁field ▁Using ▁the ▁above ▁definitions ▁we ▁can ▁show ▁that ▁the ▁gradient ▁of ▁a ▁second - order ▁tensor ▁field ▁in ▁cyl ind rical ▁polar ▁coordinates ▁can ▁be ▁expressed ▁as ▁ ▁D iver gence ▁of ▁a ▁second - order ▁tensor ▁field ▁The ▁diver gence ▁of ▁a ▁second - order ▁tensor ▁field ▁in ▁cyl ind rical ▁polar ▁coordinates ▁can ▁be ▁obtained ▁from ▁the ▁expression ▁for ▁the ▁gradient ▁by ▁collect ing ▁terms ▁where ▁the ▁scalar ▁product ▁of ▁the ▁two ▁outer ▁vectors ▁in ▁the ▁dy adic ▁products ▁is ▁non zero . ▁ ▁Therefore , ▁ ▁See ▁also ▁ ▁Cov ar iance ▁and ▁contra var iance ▁ ▁Basic ▁introduction ▁to ▁the ▁mathematics ▁of ▁cur ved ▁spac etime ▁ ▁Orth ogonal ▁coordinates ▁ ▁F ren et – Ser ret ▁formulas ▁ ▁Cov ari ant ▁derivative ▁ ▁T ensor ▁derivative ▁( continu um ▁mechan ics ) ▁ ▁Cur vil ine ar ▁perspective ▁ ▁Del ▁in ▁cyl ind rical ▁and ▁spher ical ▁coordinates ▁ ▁References ▁Notes ▁ ▁Further ▁reading ▁ ▁External ▁links ▁ ▁Der iv ation ▁of ▁Unit ▁V ectors ▁in ▁Cur vil ine ar ▁Co ordinates ▁ ▁Math World ' s ▁page ▁on ▁Cur