Transcription of A Basic Operations of Tensor Algebra - Springer
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A Basic Operations of Tensor Algebra - Springer
A Basic Operations of Tensor AlgebraThe Tensor calculus is a powerful tool for the description of the fundamentals in con-tinuum mechanics and the derivation of the governing equations for applied prob-lems. In general, there are two possibilities for the representation of the tensors andthe tensorial equations: the direct (symbolic, coordinate-free) notation and the index (component) notationThe direct notation operates with scalars, vectors and tensors as physical objectsdefined in the three-dimensional space (in this book we are limit ourselves to thiscase). A vector (first rank Tensor )aaais considered as a directed line segment ratherthan a triple of numbers (coordinates). A second rank tensorAAAis any finite sumof ordered vector pairsAAA=a ba ba b+.
168 A Basic Operations of Tensor Algebra of matrices for a specified coordinate system. The purpose of this Appendix is to give a brief guide to notations and rules of the tensor calculus applied through-out this book. For more comprehensive overviews on tensor calculus we recom-mend [58, 99, 126, 197, 205, 319, 343].
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