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  1. ExtravagantDreams

    Line, surface and volume integrals

    In theory one can also integrate a scalar or vector field within volume with some directional vector. This would come up if you extended the divergence theorem to a four-dimensional space.
  2. ExtravagantDreams

    Simple integral, example or general solution correct?

    Yes of course. v is the indefinate integral of v' and not over the boundary of the initial region. I should have realize this before. Thanks! Then, is there anything to be done without knowing the exact form of f(k,x)?
  3. ExtravagantDreams

    Integration by parts, can you do this?

    Yes, it's a book. Usually for graduate level, but the section on calculus of variations is just an ellaboration of what you've probably already learned. This method uses integrating along a parametized line, which is something you learn early on in vector calculus. I think what throws many...
  4. ExtravagantDreams

    Simple integral, example or general solution correct?

    Well, I'm taking u as k_x and v' as f in the standard notation \int u v' = u v| - \int u' v therefore I will not have a derivative of f. Not sure what you mean by surface term. I do realize this is an integral over three variables and I should use the divergence theorem in general. But...
  5. ExtravagantDreams

    Integration by parts, can you do this?

    So, to generalize it, \int \frac{dA}{dt}B\ dt = - \int \frac{dB}{dt}A\ dt is true if one of the functions A or B vanishes at both endpoints, which is what LCKurtz showed. You just have to remember in the variational principle A and B will be derivatives.
  6. ExtravagantDreams

    Integration by parts, can you do this?

    You derivation is not quite correct. I would advise you to see Goldstein (Classical Mechanics). It has a thorough explanation of Lagrangian mechanics starting with the variational principle. You will be making variations with respect to \varepsilon , using x(t, \varepsilon ) = x(t, 0) +...
  7. ExtravagantDreams

    Simple integral, example or general solution correct?

    This should be very simple, but I can find a simple example that violates my general conclusion. I clearly must be doing something wrong with my integration by parts. Any suggestions would be great. Define a distribution such that the density; \eta(\vec{x})=\int d\vec{k} f(\vec{x},\vec{k})...
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