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Level Sets ü A Function of Two Variables : F @x , y D = x 2 + y 2 Represents a Surface

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Level Sets

ü A Function of Two Variables : F @x , yD = x2 + y2 Represents a Surface

Intersect the Surface with a Plane at a Height above the xy-plane

2 Level Sets -- Slide Show.nb

Page 3: Level Sets -- Slide Show - Northeastern Universitymathserver.neu.edu/~eigen/1252DIR/Level Sets -- Slide Show.pdf · Intersect the Surface with a Plane at a Height above the xy-plane

The Plane DRAWS a curve on the Surface

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Level Sets -- Slide Show.nb 3

Page 4: Level Sets -- Slide Show - Northeastern Universitymathserver.neu.edu/~eigen/1252DIR/Level Sets -- Slide Show.pdf · Intersect the Surface with a Plane at a Height above the xy-plane

Project the curve on the surface onto the xy-planeThis gives the Level Curve in the xy-plane

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4 Level Sets -- Slide Show.nb

Page 5: Level Sets -- Slide Show - Northeastern Universitymathserver.neu.edu/~eigen/1252DIR/Level Sets -- Slide Show.pdf · Intersect the Surface with a Plane at a Height above the xy-plane

Add more Level Curves

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Level Sets -- Slide Show.nb 5

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