Retrieving "Manifold (m)" from the archives

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1. Vector Field

   Linked via "manifold (M)"

   A vector field is a mathematical construction that assigns a vector to every point in a subset of Euclidean space $\mathbb{R}^n$, or more generally, to every point in a differentiable manifold (M)/). It is a fundamental concept in mathematical physics, particularly in the study of continuum mechanics, electromagnetism's Maxwell's Equations, and fluid dynamics. While conceptually straightforward—a field of arrows—its analytical properties, such …