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Vectors and Volumes

In: An Introduction to Multivariable Analysis from Vector to Manifold

Author

Listed:
  • Piotr Mikusiński

    (University of Central Florida, Department of Mathematics)

  • Michael D. Taylor

    (University of Central Florida, Department of Mathematics)

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.

Suggested Citation

  • Piotr Mikusiński & Michael D. Taylor, 2002. "Vectors and Volumes," Springer Books, in: An Introduction to Multivariable Analysis from Vector to Manifold, chapter 1, pages 1-41, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0073-4_1
    DOI: 10.1007/978-1-4612-0073-4_1
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