Vectors and Volumes

Piotr Mikusiński and Michael D. Taylor
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Piotr Mikusiński: University of Central Florida, Department of Mathematics
Michael D. Taylor: University of Central Florida, Department of Mathematics

Chapter 1 in An Introduction to Multivariable Analysis from Vector to Manifold, 2002, pp 1-41 from Springer

Abstract: Abstract ℝ3, the set of ordered triples (x1,x2,x3) of real numbers, is a natural and useful model for physical space. Similarly, ℝ4 is an obvious model for space-time. More generally, problems in the sciences or engineering that involve N variables are often investigated in the setting of ℝ N . Such problems often require the Standard ideas of analysis: continuous change, instantaneous rates of change, integration, and so forth. To adapt these concepts from a one dimensional to an N-dimensional setting, it is first helpful to introduce some algebraic structure on ℝ N , the structure of a vector space, and then to consider transformations of Euclidean N-dimensional Spaces, particularly the simple and very useful ones known as linear transformations.

Keywords: Vector Space; Linear Transformation; Linear Subspace; Vector Space Versus; Linear Independence (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-1-4612-0073-4_1

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