14.1 Level Curves and Contour Map
Level Curves
We consider functions of two variables of the form . The domain of z is the set of all in the xy-plane for which is defined.
The graph of is a surface in 3D. You can sketch the graph of any function by typing in the box below.
Definition:- The level curves of a function f of two variables are the curves with equations , where is a constant (in the range of f).
A level curve f(x,y)= = k is the set of all points in the domain of f at which f takes on the given value k.
In other words, it is a curve in the xy-plane that shows where the graph of f has height k (above or
below the xy-plane).
You can sketch these level curves by typing their equations in the given boxes.
A collection of level curves is called a contour map.