Vector analysis, also known as vector calculus, is an advanced branch of mathematics that expands calculus concepts to multiple dimensions. It deals with vector fields and their derivatives and integrals and is closely connected with multivariable calculus. Key concepts of vector analysis including gradients, divergences, and curls, alongside operations such as line integrals, surface integrals, and volume integrals are commonly applied in science research.
Josiah W. Gibbs is one of the most important contributors to vector analysis. Gibbs named and introduced the notations of dot and cross products of vectors and facilitated the publicization of vector field as well as the use of the vectorial approach instead of the quaternion approach in physical research.
