Vectors

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Table of Contents

  1. Introduction
  2. Vector Algebra
  3. Vector Calculus

Readers

This wikibook introduces three-dimensional vectors as mathematical entities, though their application will be found, very likely, in physical science. For examples, velocity and acceleration of a particle in a reference frame are usually defined as vectors. As this is an elementary mathematical textbook, it is useful to state the prerequisites for readers expecting to benefit from what is written. When faced with listing prerequisites for a similar textbook in 1965, James A. Hummel of University of Maryland gave this list: Basic concepts of trigonometry, of Cartesian coordinates in the plane, and of set theory and notation. For his text he also required knowledge of the definition of a function, of the definition and properties of determinants of orders two and three, the absolute value, the field axioms, and the order axioms for real numbers.

Study of the vector algebra in this wikibook is good preparation for Linear Algebra. For students that have studied calculus of one variable, the chapter on vector analysis provides an introduction to the tools physicists use to study vector fields dependent on position in space.

Consider the set of directed line segments in the plane. If two such segments are parallel, equal in length, and similarly directed, they are said to be equipollent. Such segments can be considered equivalent, and the collection of equivalence classes of directed segments in the plane provides an illustration of a planar space of vectors.

For an alternative textbook, readers may refer to w: Vector Analysis (1901) by J. W. Gibbs and E. B. Wilson. This venerable textbook is credited with distilling dispersed concepts into a course in mathematics that supported students of physics and engineering. In the century since its publication many imitators, including this wikibook, have perpetuated its language and notation.