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Classical notation for line integrals

  1. Nov 26, 2007 #1
    I don't really understand the classical notation for line integrals, namely why would you want to represent a scalar function f(x,y) as p(x,y)dx + q(x,y)dy. I also don't fully understand the geometrical interpretation of this. Though solving the problems is easy, I don't really understand what it means. The notation f(x,y)ds seems far more intuitive to me. Can anyone link me to a geometrical interpretation for the classical notation of line integrals? Thanks.
     
  2. jcsd
  3. Nov 26, 2007 #2
    Its because [tex] A \ dx + B \ dy [/tex] is known as a one-form. In this case [tex] A = p(x,y) [/tex] aand [tex] B = q(x,y) [/tex]. Think of it like this: If there is unit displacement in the x-direction then A units of work is done. If there is a unit displacement in the y-direction then B units of work is done.
     
    Last edited: Nov 26, 2007
  4. Nov 26, 2007 #3
    Ahh, thanks. This helps me make sense out of what was going on.
     
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