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.
KeywordsStationary Point Tensor Field Piezoelectric Body Antiresonant Frequency Asymptotic Sense
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