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Unformatted text preview: L ( f,c ) with R is the graph of a C 1 function φ ( x,y ) , de±ned on B ε (( x ,y )) and taking values in [ z − δ,z + δ ] . In other words, if −→ x = ( x,y,z ) ∈ R , then f ( x,y,z ) = c ⇐⇒ z = φ ( x,y ) . (3.23) ²urthermore, at any point ( x,y ) ∈ B ε ( −→ x ) , the partial derivatives of φ are ∂φ ∂x = − ∂f/∂x ∂f/∂z ∂φ ∂y = − ∂f/∂y ∂f/∂z (3.24) where the partial on the left is taken at ( x,y ) ∈ B ε ⊂ R 2 and the partials on the right are taken at ( x,y,φ ( x,y )) ∈ R ⊂ R 3 ....
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
- Fall '08