29-Surface, Contour Maps

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

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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 ) } .I t sa surface in 3 -space that passes the vertical line test .Bu thowcantha tsu r fa c eber ea l i z edin 2 -space, and how can apa rt icu la rrea l izat ionhe lpinunderstand ingsuchimpo rtant calculus features as slope, local extrema, and concavity? One way, of course, is to ‘picture’ the surfacejustasGoog ledoesw ith‘Streetv iew ’o r a 45

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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
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## This note was uploaded on 04/12/2011 for the course M 408d taught by Professor Sadler during the Spring '07 term at University of Texas at Austin.

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

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