MATH 2400 Lecture Notes - Lecture 12: Tangent Space, Joule, Parallelogram

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

Document Summary

Inst ructor: dr. xingzhou yang @2018 page 1 of 2. Review: normal direction of the tangent plane through po (xo , yo , zo) ( 12. 4) : Consider a general grid point pii(xi , yi) = po . fx(xi, yi) and /y (xi , yi) are the slopes of the tangent lines through ! "ii in the direction of a and b. = (- fx( xi , yj) , - fy(xi, yi) , 1) ! ::,,y = (- fx(xi, yi) , - /y(xi , yi) , 1) ! So the little area of the parallelogram tij is b. ~j = la x bl = ux(xi, yj)) 2 + (/y (xi, yi)) 2 + 1 b. a, and the total surface area is m n m n. A(s) = jim " " " " ! ::,,a m ,n-+oo _j _j i=l i=l i=l i=l p jhf. The area of the surface with eql\: . __~