10-2 ' 



MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



r A = : ^ 

 r sm 6 



, * x <*r - a ( r ' 



curie A = : s < -TT- - sm 6 ^r 



r sin [ d</> dr J ' 



cur 



5.21 Cylindrical Coordinates. 



i. 



2. 



4- 



6. 



8. 



fp, 



U'-f, 



I w = z. 



{x = p cos 6, 

 y = p sin 0, 

 2 = Z. 



I 



~ P' 



f dSV = p dd dz, 

 I dSo = dz dp, 

 (dS z = pdpdd. 

 dr = pd pd ddz. 



i 3A Z SA0 



curlpA = paT '--to' 



^cur! 9 A = ^-^. 

 dz dp 



dA 



5.22 Ellipsoidal Coordinates.. 



u, v, w are the three roots of the equation: 



OC "V 2 



I. 



I. 



a>b>c. u>v>w. 



6 = u: Ellipsoid. 

 6 = v: Hyperboloid of one sheet. 

 6 = w: Hyperboloid of two sheets. 



