Its modern form is the n-dimensional analogue of the fundamental theorem of calculus, stating that the integral over the boundary of a region R of a chain Γ equals the integral over the region R of the exterior derivative of Γ.
Its modern form is the n-dimensional analogue of the fundamental theorem of calculus, stating that the integral over the boundary of a region R of a chain Γ equals the integral over the region R of the exterior derivative of Γ. More well-known, however, is the classical form, stating that the integral – over a region R – of the curl of a vector field F dotted with the normal vector n equals the integral – over the boundary of R – of F dotted with the tangent vector t. For ten points, name this theorem of multivariable calculus, which can also be used to derive the special-case theorems of Gauss and Green.
Its modern form is the n-dimensional analogue of the fundamental theorem of calculus, stating that the integral over the boundary of a region R of a chain Γ equals the integral over the region R of the exterior derivative of Γ.
Stokes’s Theorem