ita ▁symbol . ▁ ▁Example : ▁C yl ind rical ▁polar ▁coordinates ▁For ▁cyl ind rical ▁coordinates ▁we ▁have ▁ ▁and ▁ ▁where ▁ ▁Then ▁the ▁cov ari ant ▁and ▁cont rav ari ant ▁basis ▁vectors ▁are ▁ ▁where ▁ ▁are ▁the ▁unit ▁vectors ▁in ▁the ▁ ▁directions . ▁ ▁Note ▁that ▁the ▁components ▁of ▁the ▁metric ▁tensor ▁are ▁such ▁that ▁ ▁which ▁shows ▁that ▁the ▁basis ▁is ▁orthogonal . ▁ ▁The ▁non - zero ▁components ▁of ▁the ▁Christ off el ▁symbol ▁of ▁the ▁second ▁kind ▁are ▁ ▁Represent ing ▁a ▁physical ▁vector ▁field ▁The ▁normal ized ▁cont rav ari ant ▁basis ▁vectors ▁in ▁cyl ind rical ▁polar ▁coordinates ▁are ▁ ▁and ▁the ▁physical ▁components ▁of ▁a ▁vector ▁v ▁are ▁ ▁Grad ient ▁of ▁a ▁scalar ▁field ▁The ▁gradient ▁of ▁a ▁scalar ▁field , ▁f ( x ), ▁in ▁cyl ind rical ▁coordinates ▁can ▁now ▁be ▁computed ▁from ▁the ▁general ▁expression ▁in ▁cur vil ine ar ▁coordinates ▁and ▁has ▁the ▁form ▁ ▁Grad ient ▁of ▁a ▁vector ▁field ▁Similarly , ▁the ▁gradient ▁of ▁a ▁vector ▁field , ▁v ( x ), ▁in ▁cyl ind rical ▁coordinates ▁can ▁be ▁shown ▁to ▁be ▁ ▁D iver gence ▁of ▁a ▁vector ▁field ▁Using ▁the ▁equation ▁for ▁the ▁diver gence ▁of ▁a ▁vector ▁field ▁in ▁cur vil ine ar ▁coordinates , ▁the ▁diver gence ▁in ▁cyl ind rical ▁coordinates ▁can ▁be ▁shown ▁to ▁be ▁ ▁Lap la cian ▁of ▁a ▁scalar ▁field ▁The ▁Lap la cian ▁is ▁more ▁easily ▁computed ▁by ▁not ing ▁that ▁. ▁ ▁In