Math 251 Lecture 19: Monday, October 25th 1999.
Today we continued with section 12.6 by looking at the extension
of the directional derivative to 3 variables, and
the extension of the gradient vector to 3
variables. An example involving a temperature distribution in
3-space was worked out.
Next we showed that the gradient vector is
perpendicular to the tangents to every spacecurve going
through a point in a level surface. This fact was used to
obtain formulae for the tangent plane to a level surface,
and the corresponding normal line.
To illustrate, a tangent plane and normal line to an ellipsoid
was plotted using Maple.
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lec_notes /
lec19.html
Revised 26 October 1999 by
John Hebron.