PHYS358 Lecture Notes - Lecture 1: Partial Derivative, R V R, Total Derivative

• School: University of Waterloo
• Department: Physics
• Course: PHYS358
• Professor: James Martin

Document Summary

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 df = n. 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.