ABSTRACT
This chapter gives a review of mathematical relations which will prove to be useful in the subsequent chapters. A more complete development is given in Chandrasekharaiah and Debnath (1994).
Unless otherwise noted, repeated Latin indices will imply summation over the range 1 to 3. For example,
aibi ¼ a1b1 þ a2b2 þ a3b3 (2:1)
aijbjk ¼ ai1b1k þ ai2b2k þ ai3b3k (2:2)
The repeated index is ‘‘summed out’’ and therefore ‘‘dummy’’. The quantity aijbjk in Equation 2.2 has two free indices i and k (and later will be shown to be the ikth entry of a second-order tensor). Note that Greek indices do not imply summation. Thus aaba¼ a1b1 if a¼ 1.
