The VectorCalculus package is a collection of commands that perform multivariate and vector calculus operations.

Multivariate calculus refers to the calculus of functions from $R^n$ to $R$. Vector calculus refers to the calculus of functions from $R^n$ to $R^m$, where $1<m$.

The VectorCalculus package contains a large set of predefined coordinate systems. All computations in the package can be performed in any of these coordinate systems.  By default, the Cartesian coordinate system is used.  The basic objects on which the commands in the VectorCalculus package operate are Vectors, vector fields, and scalar functions.

For a complete list of the routines in the VectorCalculus package and advanced information on the capabilities of this package, see the Details of the VectorCalculus package help page.

Each command in the VectorCalculus package can be accessed by using either the long form or the short form of the command name in the command calling sequence.  For more information, see the Using Packages help page.

Long form

VectorCalculus:-CrossProduct(<a, b, c>, <d, e, f>);

Short form

with(VectorCalculus):

CrossProduct(<a, b, c>, <d, e, f>);

Some routines in the VectorCalculus package come with a task template to step you through the process of solving a vector calculus problem. For more information, see the Using Tasks help page.

For students learning the concepts presented in an introductory vector calculus course, see the Student:-VectorCalculus help page.