The Surface Area formula for Parametric Surfaces // Vector Calculus

Published: 25 November 2020
on channel: Dr. Trefor Bazett
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In this video we derive the formula to compute surface area given some surface described parametrically. Thus if you have a parametric description, all you need to do is plug it into this formula. The derivation works by looking at a tiny section of surface area, and approximating this with a little tangential parallelogram whose area can be computed by the length of the cross product of r_u Delta u and r_v Delta b, the partial derivatives of the position vector with respect to the two parameters u and v. Thus the integral is effectively just summing up these little surface areas and becomes a double integral of the length of that cross product. We will see a concrete example of this in the next video in the vector calculus playlit.

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Watch video The Surface Area formula for Parametric Surfaces // Vector Calculus online without registration, duration hours minute second in high quality. This video was added by user Dr. Trefor Bazett 25 November 2020, don't forget to share it with your friends and acquaintances, it has been viewed on our site 68,034 once and liked it 2.1 thousand people.