This textbook used vector calculus systematically to solve problems of celestial mechanics.

Partial derivatives are used in vector calculus and differential geometry.

Field lines can be used to trace familiar quantities from vector calculus:

The development of vector calculus was Gibbs's other great contribution to mathematics.

The term "curve" is more common in vector calculus and differential geometry.

A proof using vector calculus is shown in the box below.

In this case the content is just that of the cross product of traditional vector calculus.

The four most important differential operations in vector calculus are:

These structures give rise to a volume form, and also the cross product, which is used pervasively in vector calculus.

There are two important alternative generalizations of vector calculus.