Divergence calculus. Understand vector flux through closed surfaces, verify proofs, and see practical examples for multivariable calculus. In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters the volume in an infinitesimal neighborhood of each point. Explore the Gauss-Ostrogradsky Divergence Theorem with our interactive calculator. There are 2 steps to solve this one. Stokes' theorem, [1] also known as the Kelvin–Stokes theorem[2][3] after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem, [4] or rotor theorem is a theorem in vector calculus on three-dimensional Euclidean space and real coordinate space, [note 1]. The divergence is a scalar operator applied to a 3D vector field, while the curl is a vector operator that measures the rotation of the field in three-dimensional space. Feb 26, 2002 · Different Operations using Del – Divergence 29 When the del operator takes the divergence of a vector field, it results in a scalar field that tells us how much the field spreads out or converges at each point in space. Oct 25, 2025 · Divergence and Curl are differential operators in vector calculus. Adams and Christopher Essex. Comprehensive calculus textbook covering differentiation, integration, and advanced topics.