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.
关键词
Stokes公式/微分形式/第二类曲面积分
Key words
Stokes'theorem/differential form/surface integral of the second type