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This appendix contains a brief outline of vector algebra and vector calculus. The essential purpose of *vector algebra*
is to convert the propositions of Euclidean geometry in three-dimensional
space into a convenient algebraic form. *Vector calculus* allows us to define
the instantaneous velocity and acceleration of a moving object in three-dimensional space, as
well as the work done when such an object travels along a general
curved trajectory in a force field. Vector calculus also introduces the concept of a *scalar
field*: *e.g.*, the potential energy associated with a conservative force field.

Richard Fitzpatrick
2011-03-31