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revision 4344 by jfenwick, Wed Feb 27 03:42:40 2013 UTC revision 4345 by jfenwick, Fri Mar 29 07:09:41 2013 UTC
# Line 14  Line 14 
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15  \chapter{The Einstein Summation Convention}  \chapter{The Einstein Summation Convention}
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17  The Einstein Summation Convention (ESC) is a notational convention that is prefered by the \esc developers. It is a condensed and practical way to deal with multi-dimensional and convoluted PDEs. By suppressing the need to write out the many terms of each problem it is possible to increase efficiency and reduce the number of errors created through poor working. According to the convention, when an index variable appears twice in a single term, it implies that we are summing over all of its possible values.  The Einstein Summation Convention (ESC) is a notational convention that is preferred by the \esc developers. It is a condensed and practical way to deal with multi-dimensional and convoluted PDEs. By suppressing the need to write out the many terms of each problem it is possible to increase efficiency and reduce the number of errors created through poor working. According to the convention, when an index variable appears twice in a single term, it implies that we are summing over all of its possible values.
18  So we have;  So we have;
19  \begin{equation}  \begin{equation}
20  a_{1}\frac{\partial^2 f}{\partial x_{1}^2} + a_{2}\frac{\partial^2 f}{\partial x_{2}^2} = a_{i}\frac{\partial^2 f}{\partial x_{i}^2}  a_{1}\frac{\partial^2 f}{\partial x_{1}^2} + a_{2}\frac{\partial^2 f}{\partial x_{2}^2} = a_{i}\frac{\partial^2 f}{\partial x_{i}^2}

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