Main Concept

A level curve of the surface $z \= f\left(x\, y\right)$ is a two-dimensional curve with the equation $f\left(x\, y\right) \= k$, where k is a constant in the range of f. A level curve can be described as the intersection of the horizontal plane $z \= k$ with the surface defined by f. Level curves are also known as contour lines.

A vertical cross section (parallel to a coordinate plane) of a surface $z \= f\left(x\, y\right)$ is a two-dimensional curve with either the equation $z \= f\left(c\, y\right)$ or the equation $z \= f\left(x\, d\right)$, where c and d are constants. Such a cross section can be described as the intersection of a vertical plane $x \= c$ or $y \=d$ with the surface defined by f.

Both level curves and cross sections are helpful for visualizing and plotting multivariate functions.

More MathApps

MathApps/Calculus