MATH 2321 Lecture Notes - Lecture 8: Level Set, Farad

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

Document Summary

Ex, z= f(x,y) = x + y2 -> paraboloid. Tp bowl shape the level curve where f= 7 (i. e. k=?) is x2 + y2 = 7 which is a circle of radius is (x2 + y2 = r2). (in a plane of 2=7) "z= constant" represents a horizontal plane parallel to the xy-plane (3) for a real-valued func of 3 variables, w=f(x, y, z), the lever et where f = k is called a level surface. Y = f(x) f: ir - ir xmy graph of y=f(x) = {(x,y)) y = f(x)} Y=x? u xiys graph = {x,y) y=x+} in r? (2) z = f(x,y): r=r | graph = {(x,y,3)/2 = f(x,y)} in r3. Ex. z = f(x, y) = x + y : rsr (x,y) z. 3 f : r^~ro (4. ,,xn) (y,m,n) graph = {(x,x2,-/m, 45%. n)|(9,5%): f(x,-. (in rhop) Ex. (1) f: r=r given by f(x, y) = x - y2 (x,y) az=f(x, y) = x2-y2.