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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

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