▁the ▁definition ▁of ▁the ▁Lam é ▁coefficients , ▁▁ ▁and ▁thus ▁▁ ▁Now , ▁since ▁ ▁when ▁, ▁we ▁have ▁▁ ▁and ▁we ▁can ▁proceed ▁normally . ▁ ▁Sur face ▁integr als ▁Like wise , ▁if ▁we ▁are ▁interested ▁in ▁a ▁surface ▁integral , ▁the ▁relevant ▁calculation , ▁with ▁the ▁parameter ization ▁of ▁the ▁surface ▁in ▁Cart esian ▁coordinates ▁is : ▁▁ ▁Again , ▁in ▁cur vil ine ar ▁coordinates , ▁we ▁have ▁▁ ▁and ▁we ▁make ▁use ▁of ▁the ▁definition ▁of ▁cur vil ine ar ▁coordinates ▁again ▁to ▁yield ▁▁▁ ▁Therefore , ▁▁ ▁where ▁ ▁is ▁the ▁permut ation ▁symbol . ▁ ▁In ▁determin ant ▁form , ▁ ▁the ▁cross ▁product ▁in ▁terms ▁of ▁cur vil ine ar ▁coordinates ▁will ▁be : ▁ ▁Grad , ▁curl , ▁div , ▁Lap la cian ▁ ▁In ▁orthogonal ▁cur vil ine ar ▁coordinates ▁of ▁ 3 ▁dimensions , ▁where ▁▁ ▁one ▁can ▁express ▁the ▁gradient ▁of ▁a ▁scalar ▁or ▁vector ▁field ▁as ▁ ▁For ▁an ▁orthogonal ▁basis ▁ ▁The ▁diver gence ▁of ▁a ▁vector ▁field ▁can ▁then ▁be ▁written ▁as ▁ ▁Also , ▁ ▁Therefore , ▁ ▁We ▁can ▁get ▁an ▁expression ▁for ▁the ▁Lap la cian ▁in ▁a ▁similar ▁manner ▁by ▁not ing ▁that ▁ ▁Then ▁we ▁have ▁ ▁The ▁expressions ▁for ▁the ▁gradient , ▁diver gence , ▁and ▁Lap la cian ▁can ▁be ▁directly ▁extended ▁to ▁n - dim ensions . ▁ ▁The ▁curl ▁of ▁a ▁vector ▁field ▁is ▁given ▁by ▁▁ ▁where ▁ ε ijk ▁is ▁the ▁Le vi - C iv