Vectors in three-dimensional space

Vectors in three-dimensional space (1978) is a book concerned with physical quantities defined in "ordinary" 3-space. It was written by J.S.R.Chisholm, an English mathematical physicist, and published by Cambridge University Press . According to the author, such physical quantities are studied in Newtonian mechanics, fluid mechanics, theories of elasticity and plasticity, non-relativistic quantum mechanics, and many parts of solid state physics. The author further states that "the vector concept developed in two different ways: in a wide variety of physical applications, vector notation and techniques became, by the middle of this century, almost universal; on the other hand, pure mathematicians reduced vector algebra to an axiomatic system, and introduced wide generalisations of the concept of a three-dimensional 'vector space'." Chisholm explains that since these two developments proceeded largely independently, there is a need to show how one can be applied to the other.

Summary

Vectors in three-dimensional space has six chapters, each divided into five or more subsections. The first on linear spaces and displacements including these sections: Introduction, Scalar multiplication of vectors, Addition and subtraction of vectors, Displacements in Euclidean space, Geometrical applications. The second on Scalar products and components including these sections: Scalar products, Linear dependence and dimension, Components of a vector, Geometrical applications, Coordinate systems. The third on Other products of vectors. The last three chapters round out Chisholm's integration of these two largely independent developments.

References

• Vectors in three-dimensional space has been cited by the 2002 Encyclopedia Americana article on Vector Analysis
• Chisholm, J.S.R. Vectors in three-dimensional space, Cambridge University Press, 1978, ISBN:0-521-29289-1