Multivariable Calculus
Most physical systems are characterized by more than two quantitative variables. Experience has shown that it is not always possible to change such quantities at will, but that specification of some of them will determine definite values for others. Functional relations involving three or more variables lead us to branches of calculus which make use of partial derivatives and multiple integrals.
11.1 Partial Derivatives
We have already snuck in the concept of partial differentiation in several instances by evaluating the derivative with respect to x of a function of the form 
, while treating as if they were constant ...
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