Home / All Definitions / Calculus / Vector Calculus Definition

Vector calculus or vector analysis is the use of calculus (limits, derivatives, and integrals) with two or more independent variables, or two or more dependent variables. This can be thought of as the calculus of three dimensional figures. Vector calculus is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space R^{3}. The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration. Common elements of multivariable calculus include parametric equations, vectors, partial derivatives, multiple integrals, line integrals, and surface integrals. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields and fluid flow.

Vector calculus was developed from quaternion analysis by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, Vector Analysis. In the conventional form using cross products, vector calculus does not generalize to higher dimensions, while the alternative approach of geometric algebra, which uses exterior products does generalize.

“Vector Calculus.” Wikipedia, Wikimedia Foundation, 19 Apr. 2020, en.wikipedia.org/wiki/Vector_calculus.

Check out our free app for iOS & Android.

For more information about our app visit here!

Add Math Converse as app to your home screen.

Check out our free desktop application for macOS, Windows & Linux.

For more information about our desktop application visit here!

Check out our free browser extension for Chrome, Firefox, Edge, Safari, & Opera.

For more information about our browser extension visit here!

Placeholder

Placeholder