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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