Level Curves and Cross Sections - Maple Help

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Level Curves and Cross Sections

Main Concept

A level curve of the surface z = fx, y is a two-dimensional curve with the equation fx, y = 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 = fx, y is a two-dimensional curve with either the equation z = fc, y or the equation z = fx, d, 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.

 

Select a function from the drop-down menu or type your own function in the text box below and click "Enter" to plot it. Click the radio buttons to view either a level curve or a cross section. Use the slider to change the value of the related constant k, c, or d.  Click "Reset" to reset both plots.

 

z = f(x, y) =

 =

 

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