C-1 



APPENDIX C 



NOTATION 



The Cartesian coordinate system is usually designated by (xi,Xa,X3), 

 and the resulting position vector x has length x. Occasionally, especially if 

 one coordinate direction has particular significance, we use the coordinates 

 (x, y, z), designate the position vector by r and its length by r. Differentiation 

 with respect to a spatial coordinate is designated either by comma (tensor notation) 

 or by explicit differentiation signs, e.g. : 



d p _ B p 



f5 X SX3 



= P: 



Repeated subscripts should be summed over, in the usual tensor notation fashion. 

 If u = (ui , U.J , 113) = (u^, Uy, u^.) is the velocity field, its divergence is given by: 



b u 3 u S u 



div u = V-u = u. .=u, ,,+uo,3+U3,3 =^; — + -^— ^ + ^^ — 

 — — 1,1^'- oxoy dz 



When there can be no confusion, differentiation with respect to time is occasionally 

 indicated as a subscript t : 



S 



P _ 



St P,t ^ Pt 



The same might be done for differentiation with respect to x, y or z, e.g. , the 

 one -dimensional wave equation: 



P 1 S^ p 1 



-*- ~ §- becomes p = —2- P 



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