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Guide to Essential Math, 2nd Edition by Sy M. Blinder

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Chapter 12

Vector Analysis

The perceptible physical world is three dimensional (although additional hidden dimensions have been speculated in superstring theories and the like). The most general mathematical representations of physical laws should therefore be relations involving three dimensions. Such equations can be compactly expressed in terms of vectors. Vector analysis is particularly applicable in formulating the laws of electromagnetic theory.

12.1 Scalars and Vectors

A scalar is a quantity which is completely described by its magnitude—a numerical value and usually a unit. Mass and temperature are scalars, with values, for example, like 10 kg and 300 K. A vector has, in addition, a direction. Velocity and force are vector quantities. A ...

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