Labware - MA35 Multivariable Calculus - Three Variable Calculus



Level Sets & Contour Surfaces


A contour of a function f(x,y,z) is obtained by setting w = k constant where w = f(x,y,z). The resulting surface f(x,y,z) = k is a contour in the domain of f.

A set of contours in either the two or three variable case is called a level set. Level sets that have singularities are especially interesting since the hypersurface has critical points at these values of k.



  • Use the tapedeck controllers to analyze the different level sets of the function f. What can you say about critical points of the hypersurface f(x,y,z)?