vector field

vector field : In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a subset of Euclidean space. Vector fields are often used in physics to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point. In the rigorous mathematical treatment, (tangent) vector fields are defined on manifolds as sections of a manifold's tangent bundle. They are one kind of tensor field on the manifold. Given a subset S in R n, a vector field is represented by a vector-valued function $V:\; S\; \backslash to\; \backslash mathbf\{R\}^n$ in standard Cartesian coordinates ( x 1, ..., x n). If S is an open set, then V is a continuous function provided that each component of V is continuous, and more generally V is C k vector field if each component V is k times continuously differentiable. A vec....   More from Wikipedia

vector field : A projective vector field ( projective) is a smooth vector field on a semi Riemannian manifold (p.ex. spacetime) $M$ whose flow preserves the geodesic structure of $M$ without necessarily preserving the affine parameter of any geodesic. More intuitively, the flow of..   More from Wikipedia

  A short video explaining the Gradient Vector Field, a difficult part in understing vector Calculus. Hope you enjoy it. Check out www.gaussianmath.com for more vector calculus. Thanks!

  Vector Fields - Sketching In this video, I give the definition of a 2d and 3d vector field, and do one example of roughly sketching a vector field. For more free math videos, visit JustMathTutoring.com