This preview shows pages 1–2. Sign up to view the full content.
LESSON 22
Surface Integrals of Vector Fields
READ:
Section 17.5
NOTES:
In this section we will be talking about surface integrals
RR
S
g
(
x,y,z
)
dS
of vector ﬁelds. We will restrict
ourselves to a certain type of surface: ones that have two sides. You might think that all surfaces have two
sides, but that is not the case. The M¨obius strip described on page 980 of the text is a surface with only
one side. For a two sided surface, it is possible to paint the surface with say red and blue paint in such a
way that we cannot get from the red part to the blue part without crossing a boundary curve of the surface.
Such a painting of the M¨obius strip is not possible. You might want to make a M¨obius strip for yourself to
be really convinced of that surprising fact.
As mentioned before, for a line integral, there was a nice geometric interpretation. The value of the line
integral gave the area of a curvy fence. There is no such nice geometric interpretation for surface integrals.
However, there is a physical interpretation that give us a little grasp of reality and meaningfulness for the
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Winter '11
 JerryMetzger
 Calculus, Integrals

Click to edit the document details