... parameters.1
Some material for this section appeared in the previous lecture notes. 
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... $ y(\vec{x})$2
A functional is a function of a function; in this case, it takes a function and maps it to a scalar which is numerically equal to the total free energy of the system 
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... shown3
See last lecture for details. However, it is not important that you know the mathematics, only the concepts. 
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