If a smooth example of these things is of the class C super r, meaning r times continuously differentiable, then a diffeomorphism from the class C super r can be used to rectify it. A tangent example of these things is a section of the tangent bundle of a differentiable manifold. A line tangent to one of these things at every point is an integral curve. If these things satisfy the conditions of Helmholtz's theorem, they can be written as the sum of an (*) irrotational and a solenoidal component, using the gradient and c
If a smooth example of these things is of the class C super r, meaning r times continuously differentiable, then a diffeomorphism from the class C super r can be used to rectify it. A tangent example of these things is a section of the tangent bundle of a differentiable manifold. A line tangent to one of these things at every point is an integral curve. If these things satisfy the conditions of Helmholtz's theorem, they can be written as the sum of an (*) irrotational and a solenoidal component, using the gradient and curl operators. Their line integral along a curve is equal to the dot product of these things evaluated along the curve and the differential of the parametrized curve. For 10 points, name these constructs that assign a direction and magnitude to every point in a space.
If a smooth example of these things is of the class C super r, meaning r times continuously differentiable, then a diffeomorphism from the class C super r can be used to rectify it.
vector field [or: direction field, slope field; prompt on: "vector point function", "vector-valued function", "smooth map"; anti-prompt on: "flow field", "velocity field", "force field"]