14.1 Level Curves and Contour Map

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

Information: 14.1 Level Curves and Contour Map