35-3
Chapter One
Notation - Matrices and Tensors
In this chapter, we give the definition of matrices and tensors for the purpose of notation used
in the book. We summarize the basic relations that are useful for reading the text, without
any proofs or in-depth presentation. More details are given on the web (Theory, Chapter 1,
Examples, Chapter 1). For further reading the reader should consult books specialized to this
topic (e.g. Fung 1965, Malvern 1969, Mase & Mase 1999).
1.1 Matrix representation of mathematical objects
For some physical quantities, a single number is sufficient to define the quantity. For example,
we use T to denote temperature at a given material point, and associate a certain value with
T (e.g. T = 20 °C). The quantity specified by a single number is called a scalar. We
will denote scalars by italic letters.
However, many quantities need more than one number to be completely defined. For
example, in order to define velocity of a particle, we need to know not only the magnitud ... read full excerpt from Computer Modeling in Bioengineering: Theoretical Background, Examples and Software ebook
