Level Sets of a Function

   The need to solve equations has played a prominent role throughout the history of mathematics and has driven much of its development. Differential calculus provides tools to study solutions of equations, especially from a qualitative point of view. It will be advantageous to visualize the solution set of a given equation as a level set. Here is the precise definition.

Move on to
  • derivatives of multivariable functions
  • level sets, the implicit function theorem and implicit differentiation

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    Read: L sub f of eta is defined to be the set of all xi in D such that f of xi equals eta Example of some of the level sets View an explanation of the relationship between the level sets of a function and its graph See in detail how this system of equations arises Review the definition of a linear map Take a look at the inverse function theorem Take a look at the implicit function theorem An example of a contour map A quadratic polynomial whose level sets are ellipses A quadratic polynomial whose level sets are hyperbolas A quadratic polynomial whose level sets are parabolas A quadratic polynomial whose level sets are ellipsoids A quadratic polynomial whose level sets are cylinders Try out some exercises