文档介绍：lALGEBRAICOPERATIONSFORVECTORSANDTENSORSINCARTESIANCOORDINATES(sisascalar;vandwarevectors;Tisatensor;dotorcrossoperationsenclosedwithinparenthesesarescalars,thoseenclosedinbracketsarevectors)Note:Theaboveoperationsmaybegeneralizedtocylindricalcoordinatesbyreplacing(x,y,z)by(r,6,z),andtosphericalcoordinatesbyreplacing(x,y,z)by(r,6,4).-2,-1,-1,-2.**.DIFFERENTIALOPERATIONSFORSCALARS,VECTORS,ANDTENSORSINCARTESIANCOORDINATESdv,dvydv,dvZdvydux[Vxv],=---[Vxv]=---[Vxv],=ax--dydzYdzdxaYdv,dvydv,()=-+-+-dxdydzd2vzd2v,d2vZ[V2v],=[VVv],=-+-ax2+3az2dvxdvxdvx[vVv],=vx-+v-+v,--dxYdydzdvzdv,dvz[v'Vv],=vx-+v-+v,-dxYdydz~(v,v,)a(vyvx)d(v,vX)[Vvv],=-dx+------dy+-dza(vXvy)a(vYvy)~(v,v,)[],=-dx+-+-dydza(vXvz)d(vyvz)~(v,v,)[Vvv],=----dx+-+-dydzdvxduxdux(T:Vv)=rxx-dx+r-dy+rxz-dzNote:thedifferentialoperationsmaynotbesimplygeneralizedtocurvilinearcoordi-nates;---MadisonJohnWiley&Sons,,&Sons,,storedinaretrievalsystemortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanningorotherwise,exceptaspermittedunderSections107or108ofthe1976UnitedStatesCopyrightAct,withouteitherthepriorwrittenpermissionofthePublisher,orauthorizationthroughpaymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,222RosewoodDrive,Danvers,MA01923,(508)750-8400,fax(508)750-,JohnWiley&Sons,Inc.,605ThirdAvenue,NewYork,NY10158-0012,(212)850-6011,fax(212)850-6008,E-Mail:PE