2. 



CURVILINEAR COORDINATES 



' 2 = ( a ~ + u) (a 2 + v) (a- + w) 

 (a 2 -b 2 ) (a 2 -c 2 ) .' 

 , . (b 2 + u) (b 2 + ?>) (& 2 + w) 



(ft 2 - c 2 ) (a 2 - b 2 ) 

 _ (c 2 + u) (c 2 + v} (c 2 + w) 



(02 _ C 2j (2 _ C 2) 



I i'i/y y^ | l/l-/ yt/ J- M/y 



(w -)(- w) ' 



(0 - w) (v - u) 



+ w) (b 2 + w) (c 2 + w) 

 (w - u) (w - v) 



103 



4. div A = 2 



+ U) (b 2 + W) (C 2 + U) d I ,- r-7 r . \ 



( T~7 T ~ T~ V( -r W ( w) ^4 



(w - if) (w - w) 6w \ / 



A/(a 2 + z;) (6 2 + v) (c 2 + v) d 



dv 



+ 



5- 



(v - w) (u - v) 



\/(a 2 + w) (b 2 + w) (c 2 + w) 

 (u w) (v w) 



+ u) (b 2 + u) (c 2 + u] d 



'(w v) (M v) A 

 u -w) (v- w) A w \ 



(u v) (u w) 



V(a 2 + v) ( 2 + v) (be* + v) d 

 (u v) (v w) dv 



\/(a 2 + w) (b j + w) (c 2 + w) d f ,-T-T, ^~rn> m r d \ 



+ 4 7 ^-7 v T ( v (a + w) (b 2 + w) (c 2 + w) -5- I 



(a-w) (-) dw \ ! dwj 



6. 



Via 2 

 curL A = 



(a 2 + p) (6 2 + P) (c 2 + v) d 



iv( Vw ~ vAw ) 



_ t A ffl2 



V 



7- 



curL A = 



UA = 



u w 



s 



w 



dw 



/(a 2 +u) (b 2 + u) (c 2 + u) d_ 



" V " - aw 



- w A 



(a 2 + u] (b 2 + M) (c 2 + u 

 w u 



-.V 



w 



dv 



