Vector Analysis Terms on

The following is a list of entries relating to vector analysis (or calculus) that appear on the Earliest Uses pages. Entries on the Words page are organised by letter of the alphabet. Calculus indicates there is related material on Earliest Uses of Symbols of Calculus. Vector indicates material Earliest Uses of Symbols for Vectors and Matirices.

See also the index of terms used in Matrices and Linear Allgebra.and in Calculus and Analysis

Absolute differential calculus

Convergence

Cross product

Curl

Del Calculus

Differentiable manifold

Differential

Differential form

Differential geometry

Differential topology

Directional derivative

Divergence Calculus

Divergence theorem

Dot product

Dyad

# Exact differential

## G

Gaussian curvature

Gradient Calculus

Green’s theorem

Inner product

## L

Laplace’s operator Calculus

Laplacian

Line integral

Nabla Calculus

Outer product

## P

Partial derivative Calculus

Potential function

Quaternion

## S

Scalar terms (see vector entries)

Stokes’s theorem

Surface integral

Tensor, tensor analysis, etc.

## V

Vector, vector analysis, vector space

Vector & scalar Vector

Vector analysis

Vector field

Vector triple product

History

Vector analysis was created in the late 19th century when Hamilton’s quaternion system was adapted to the needs of physics by Clifford, Tait, Maxwell, Heaviside, Gibbs and others. Many earlier results obtained by Lagrange, Gauss, Green and others on hydrodynamics, sound and electricity, were then re-expressed in terms of vector analysis.  Many of the vector analysis topics are now taught in courses on the “calculus on manifolds.”

# References

• The standard work on the origins of vector analysis (and of most of the terminology) is M. J. Crowe A History of Vector Analysis (1967, 2nd edition, 1987, Dover books). Amazon. There is a Wikipedia entry describing this book.
• There is a less exhaustive treatment in Morris Kline Mathematical Thought from Ancient to Modern Times. Oxford University Press, 1972. It is in the second volume of the reprint Amazon.
• The Encyclopedia of Mathematics entries on Vector Calculus and Vector Analysis are useful.

John Aldrich, University of Southampton, Southampton, UK. (home). Most recent changes May 2009. 