{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

29-Surface, Contour Maps

# 29-Surface, Contour Maps - Surfaces Contour Maps John E...

This preview shows pages 1–3. Sign up to view the full content.

Surfaces, Contour Maps John E. Gilbert, Heather Van Ligten, and Benni Goetz The graph of a function z = f ( x, y ) is the set of all points { ( x, y, f ( x, y ) } . It’s a surface in 3 -space that passes the vertical line test . But how can that surface be realized in 2 -space, and how can a particular realization help in understanding such important calculus features as slope, local extrema, and concavity? One way, of course, is to ‘picture’ the surface just as Google does with ‘Street view’ or a 45 -Earth Map view. Use Google Maps to see how this works near to where you live! For example, the surface to the right is the graph of z = sin( x ) sin( y ) , - π x, y π . If di ff erentiation tells us about slope, how can we express the slope at points on this surface, say at the three dots or at the origin? Thinking of the surface as mountains and valleys, the slope will be positive when we are going uphill and negative when we are going downhill. The locations of local maxima and minima are clear from the picture, and doesn’t the surface near the origin look like a ’Saddle’. What’s the slope at the origin? It depends on the direction you are walking! y z x

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
But a Google map of mountains and valleys, like the one to the right of part of Yosemite, also represents the surface as a contour map with the contours labelled by height. Recall that, for
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 6

29-Surface, Contour Maps - Surfaces Contour Maps John E...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online