PHYS 358- Final Exam Guide - Comprehensive Notes for the exam ( 45 pages long!)
30 Nov 2017
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In a similar fashion, we can consider the di erential variation of a multivariable function f (x, y) under di erential variations dx and dy. df = In general for functions of n variables f (x1, . , xn) we get that the di erential of the function is n df = We are going to introduce additional notation that may seem redundant at this point but that it is crucial when we have nested dependencies and related di erential forms. Every time that we write down a partial derivative of a function of more than one variable, we are going to specify which variables remain constant with the following notation (cid:18) f. X(cid:19)y means the partial derivative of f keeping y constant. To see how this notation is not trivial let us consider a simple example. Let then f (x, y, z) = x + y + z, y(z) = z2.
