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Transcript
Slide 1

17
VECTOR CALCULUS
VECTOR CALCULUS
The main results of this chapter are
all higher-dimensional versions of the
Fundamental Theorem of Calculus (FTC).
To help you remember them, we collect them
here (without hypotheses) so that you can see
more easily their essential similarity.
VECTOR CALCULUS
17.10
Summary
In this section, we will:
Summarize the key theorems
learned in this chapter.
SUMMARY
In each case, notice that:
On the left side, we have an integral of
a “derivative” over a region.
The right side involves the values of
the original function only on the boundary
of the region.
FTC
b
a
F ' x dx F b F a
FT FOR LINE INTEGRALS
C
f dr f r b f r a
GREEN’S THEOREM
Q P
dA
P
dx
Q
dy
D x y C
STOKES’ THEOREM
curl
F
d
S
F
d
r
C
S
DIVERGENCE THEOREM
div
F
dV
F
d
S
E
S