MATH 2321 Lecture Notes - Lecture 18: Level Set, Tangent Space, Hyperbola

• School: Northeastern University
• Department: Mathematics
• Course: MATH 2321
• Professor: Sumi Seo

Document Summary

A note: the tangent line to the level curve 1/30/19. _ at point ip = (a,b) is given by fx (a, b) (x-2) + fy (a, b)(y-6)=0) Kaib) lever = (5x (a,b), ey (a,b) (x-a, 4-6)=0" i m . The tangent plane to the level surface at point ip = (a,b,c) is. I given by [fx (a, b,c) (x-a) + fu (a, b, c)(y-b) + f(9,6, c)(z-c)=0) R o 5 f (a,b,c). (x-2)=0 where x (x, y, z), p = (a,b,c). i ex. Ep w = f(x, y, z) = xey?+ 2? yasy. F(x,y, z) = x + y2-z=o is the level surface where p=0. When (=-1, the level cure where f=-1 is x2-y&c=-1, with vertices (0, 21) F=o=> x2-y2=0 => j = ix, a pair of 2 lines, y = x 8 y=-x. The z=1 cross-section is x -y2=1 in the plane of z=1. : let m. be the level set containing point ip, then.