Encyclopedia > Vector Calculus

  Article Content

Vector calculus

Redirected from Vector Calculus

Vector calculus is a field of mathematics concerned with multivariate real analysis of vectors in 2 or more dimensions. It consists of a suite of formulas and problem solving techniques[?] very useful for engineering and physics.

We consider vector fields, which associate a vector to every point in space, and scalar fields, which associate a scalar to every point in space. For example, the temperature of a swimming pool is a scalar field: to each point we associate a scalar value of temperature. The water flow in the same pool is a vector field: to each point we associate a velocity vector.

Three operations are important in vector calculus:

measures the rate and direction of change in a scalar field; the gradient of a scalar field is a vector field.
measures a vector field's tendency to rotate about a point; the curl of a vector field is another vector field.
measures a vector field's tendency to originate from or converge upon certain points; the divergence of a vector field is a scalar field.

Most of the analytic results are more easily understood using the machinery of differential geometry, for which vector calculus forms a subset.

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
The Replacements

... Slim Dunlap played some sessions on the Pleased to Meet Me Replacements album, and then joined the band for its remaining run. Westerberg, Dunlap amd Mars have all ...