New theorems in vector calculus
نویسنده
چکیده
Two well known theorems in 3D vector calculus are Gauss’s divergence theorem (actually valid in n dimensions), and Stokes’ theorem. We find new ones. They have interesting consequences in elementary classical electromagnetism. There is a natural way to classify possible theorems of this kind and we have found every theorem the classification admits. These theorems ought to be in the usual undergraduate vector calculus and electromagnetism textbooks, but aren’t.
منابع مشابه
A new theorem in vector calculus
Two well known theorems in 3D vector calculus are Gauss’s divergence theorem (actually valid in n dimensions), and Stokes’ theorem. We present several formulations of a third natural Theorem of this ilk, which seems to have escaped previous notice.
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