Stokes’ Theorem  (continued)

 

 

In  a Nut Shell:  Stokes’ Theorem extends the “curl form” of Green’s Theorem from

two to three dimensions.  The line integral of a vector field, F,  around a simple, closed,

piecewise smooth curve, C, with positive orientation equals the curl of the vector field,

curl F, over the piecewise smooth oriented surface, S, with unit vector n .

 

 

 Stokes’ Theorem

  

    ∫ F (x,y,z) .  dr   =    ∫  ∫  curl F .  dS    =  ∫  ∫  curl F . n dS                                                                

    C                               S                              S

 

where  F (x,y,z)  is a vector field (could represent a force)

 

dr  =  the differential vector along the curve, C, in space

 

dr  =  T ds   T is the unit tangential vector to the curve, C, at any point

 

ds  =   the element of arc length along the space curve C

 

n  =  the unit normal vector to the surface, S, inside the space curve, C

 

dS = the oriented element of surface area on S

 

                           

                           

 

 

Click here to view strategies involving Stokes’ Theorem.

 

Click here to proceed to an example using Stokes’ Theorem

 

 

 



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