2006 Fall MATH 100 Lecture 22
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MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
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Definition of density function:
2006 Fall MATH 100 Lecture 22
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MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
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MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
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MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
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MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
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MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
8
MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
9
MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
10
MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
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MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
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Surface integral of vector functions, we have studied line (curve)
integral with orientation, now we go to surface with orientation.
In general, a surface is given by
G
(
x,y,z
)
=
0
The particular cones are
MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
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There are 2 unit normal vectors
A surface has 2 orientation, corresponding to the 2 normal direction.
The orientation should be chosen in the way that there is no sudden
change in the normal direction when we transverse along the surface.
MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
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The 2 possible orientation: inward normal and outward normal
MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
15
Surface integral
2006 Fall MATH 100 Lecture 22
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MATH 100 Lecture 22 Introduction to surface integrals
(continuous next page)
2006 Fall MATH 100 Lecture 22
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MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
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MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
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MATH 100 Lecture 22 Introduction to surface integrals
2006 Fall MATH 100 Lecture 22
20
MATH 100 Lecture 22 Introduction to surface integrals