All Calculus 3 Resources
Example Questions
Example Question #1 :Stokes' Theorem
LetSbe a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
为了利用斯托克斯定理,注意它的形式
The curl of a vector functionFover an oriented surfaceSis equivalent to the functionFitself integrated over the boundary curve,C, ofS.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #1 :Stokes' Theorem
LetSbe a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
为了利用斯托克斯定理,注意它的形式
The curl of a vector functionFover an oriented surfaceSis equivalent to the functionFitself integrated over the boundary curve,C, ofS.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #3 :Stokes' Theorem
LetSbe a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
为了利用斯托克斯定理,注意它的形式
The curl of a vector functionFover an oriented surfaceSis equivalent to the functionFitself integrated over the boundary curve,C, ofS.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #4 :Stokes' Theorem
LetSbe a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
为了利用斯托克斯定理,注意它的形式
The curl of a vector functionFover an oriented surfaceSis equivalent to the functionFitself integrated over the boundary curve,C, ofS.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #5 :Stokes' Theorem
LetSbe a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
为了利用斯托克斯定理,注意它的形式
The curl of a vector functionFover an oriented surfaceSis equivalent to the functionFitself integrated over the boundary curve,C, ofS.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #6 :Stokes' Theorem
LetSbe a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
为了利用斯托克斯定理,注意它的形式
The curl of a vector functionFover an oriented surfaceSis equivalent to the functionFitself integrated over the boundary curve,C, ofS.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #7 :Stokes' Theorem
LetSbe a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
为了利用斯托克斯定理,注意它的形式
The curl of a vector functionFover an oriented surfaceSis equivalent to the functionFitself integrated over the boundary curve,C, ofS.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #8 :Stokes' Theorem
LetSbe a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
为了利用斯托克斯定理,注意它的形式
The curl of a vector functionFover an oriented surfaceSis equivalent to the functionFitself integrated over the boundary curve,C, ofS.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #9 :Stokes' Theorem
LetSbe a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
为了利用斯托克斯定理,注意它的形式
The curl of a vector functionFover an oriented surfaceSis equivalent to the functionFitself integrated over the boundary curve,C, ofS.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
Example Question #1 :Stokes' Theorem
LetSbe a known surface with a boundary curve,C.
Considering the integral, utilize Stokes' Theorem to determine an equivalent integral of the form:
为了利用斯托克斯定理,注意它的形式
The curl of a vector functionFover an oriented surfaceSis equivalent to the functionFitself integrated over the boundary curve,C, ofS.
Note that
From what we're told
Meaning that
From this we can derive our curl vectors
This allows us to set up our surface integral
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