MATH 2400 Lecture Notes - Lecture 13: Conservative Vector Field, Cud, If And Only If

• School: CU-Boulder
• Department: Mathematics
• Course: MATH 2400
• Professor: Xingzhou Yang

Document Summary

Instructor: dr. xingzhou yang @2018 page 1 of 4: definition of curl: f = pi+ qj + rk = (p, q, r) is a vector field on jr3 of p , q and r exist. The curl of fis a vector field on jr3 defined by: the partial derivatives curl ff= ({jr_ 8q) i + (8p _ 8r) j + (8q _ 8p) k. The vector differential operator v ( "del") is defined as. V= i 8x + 1 fjy + k oz = \ 8x" o y " 8 z. Gr ad f = v / = t 8x +j 8y +k 8z = \ 8x " 8y " 8z. :ejj -:rjj - 8! curla =v x f" = a a a =ilay azl -jifx fzl+flfx vj/ = (ar _ 8q) i+ (ap _ 8r);+ (aq _ 8p) k ax.