Unformatted text preview: where ai and p are constants. This equation can be written as alxl+ a2z2 + a3x3 = p , 3 i=l However, we shall introduce the summation convention and write the equation above in the simple form The convention is as follows: The repetition of an index (whether superscript or subscript) in a term will denote a summation with respect to that index over its range. The range of an index i is the set of n integer values 1 to n. A lower index i, as in ai, is called a subscript, and upper index i, as in xi, is called a superscript. An index that is summed over is called a dummy index; one that is not summed out is called a free index. Since a dummy index just indicates summation, it is immaterial which symbol is used. Thus, aixa may be replaced by ajxj, etc. This is analogous 30...
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This note was uploaded on 01/04/2012 for the course ENG 501 taught by Professor Thomson during the Fall '05 term at MIT.
- Fall '05