The Degrees of Freedom inside the Stokes'Theorem and Their Applications in the Calculating of Integrals
The degrees of freedom inside the Stokes'theorem are investigated.With these degrees of freedom,two dual formulae for the second type of integrals over curved surfaces(or over general manifolds)are obtained.The first formula is for the method of integration by parts,and the second one is associated with changing the surface on which the integral is defined,respectively.An example is provided to illustrate the applications of these two formulae.
Stokes'theoremdifferential formsurface integral of the second type