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The following vector integrals are related to the curl theorem. If F=cxP(x,y,z), (1) then int_CdsxP=int_S(daxdel )xP. (2) If F=cF, (3) then int_CFds=int_Sdaxdel F. (4) The ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

A solenoidal vector field satisfies del ·B=0 (1) for every vector B, where del ·B is the divergence. If this condition is satisfied, there exists a vector A, known as the ...

Green's theorem is a vector identity which is equivalent to the curl theorem in the plane. Over a region D in the plane with boundary partialD, Green's theorem states ...

A vector field is a map f:R^n|->R^n that assigns each x a vector f(x). Several vector fields are illustrated above. A vector field is uniquely specified by giving its ...

Johnson solid J_(67).

There exists a total computable predicate P such that for any algorithm computing P(x) with running time T(x), there exists another algorithm computing P(x) with computation ...

Although the inner shaded region has the same area as the outer shaded annulus, it appears to be larger. Since the rings are equally spaced, A_(inner) = pi·3^2=9pi (1) ...

Let suma_k and sumb_k be a series with positive terms and suppose a_1<=b_1, a_2<=b_2, .... 1. If the bigger series converges, then the smaller series also converges. 2. If ...

Let P=p:q:r and U=u:v:w be distinct trilinear points, neither lying on a sideline of DeltaABC. Then the crossdifference of P and U is the point X defined by trilinears ...