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Preliminaries

  • Khanh Chau Le

Abstract

In this book we deal with vector and tensor fields on domains of the three-dimensional Euclidean point space ɛ. Elements of ɛ, called spatial points, are denoted x, y, z .... In a chosen fixed cartesian co-ordinate system a point z corresponds to a triple (z1, z2, z3), with z i being its i-th co-ordinate. The translation space of ɛ, is denoted by ν it is a three-dimensional vector space. Elements of ν are called (spatial) vectors and are denoted with boldface letters like u, v, w, .... The scalar and vector products of two vectors u, v ∈ ν are denoted u· v and u × v, respectively. Referring to the cartesian co-ordinate system there is a one-to-one correspondence between any point z and its position vector

z = z1i1 + z1i1 + z2i2 + z3i3 = z i i i

where i i (i = 1,2,3) are the standard basis vectors (Figure 2.1). Unless otherwise specified we always use the Einstein summation convention: summation on repeated indices is understood.

Keywords

Stationary Point Tensor Field Piezoelectric Body Antiresonant Frequency Asymptotic Sense 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg NewYork 1999

Authors and Affiliations

  • Khanh Chau Le
    • 1
  1. 1.Ruhr Universität BochumBochumGermany

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