Lecture (5 minutes)

There are only a few things that can be done mathematically with total differentials. They are:

  • Algebra: You can perform algebra on differentials, but you may not divide by a differential.
  • Interpret: If you have an equation for a differential, expressed in terms of differentials of variables that are independent of each other, you can interpret the factors in front of the differentials as partial derivatives.
    • Ex: If you have $dA=BdC+EdF$ and $C$ and $F$ can vary independently than $B$ can be thought of as $\left(\frac{\partial A}{\partial C}\right)_F$
  • Integrate: A differential can be integrated to find a finite change in that variable, this requires selecting a path as one would when taking a line integral.

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