CHAPTER 6 CURVILINEAR COORDINATES Example 6.6 Express in orthogonal curvilinear coordinates. 2 eˆ1   2 3  hU2 hU3 hU1 2 3 hU3 e eˆ hU1 e hU3 hU1 e hU2  2 hU2 eˆ  2 3 1 hU1 hU1 hU2 hU3 Example 6.7 2 3 at the point (5, 4, 3). 1,  , 2 3 2 32 2U 3U   2, 1, 1 hU1  hU2  hU3  2 3 1  Example 6.8 Express the heat equation  in spherical coordinates. ut 2u We have 
CHAPTER 6 CURVILINEAR COORDINATES Example 6.6 Express 2 in orthogonal curvilinear coordinates.  eˆ1 hU1  2 hU2 2  3 hU3 3 e hU1 e hU2 eˆ hU3 e hU1  2 hU2 eˆ hU3  1 hU1 hU2 hU3 2 3 hU1 Example 6.7 2 3 at the point (5, 4, 3).  1, 2  2U 2 , 3  3U 32 hU1  2, hU2  1, hU3  1 1 2 3  Example 6.8 Express the heat equation ut  2u in spherical coordinates. We have 