In their mathematics classes, students will almost always have seen functions written only in terms of the rectangular variables $x$, $y$, etc. In this case, it is always clear that the other rectangular variables are held constant in the partial derivative. $$\frac{\partial f}{\partial x} \qquad\hbox{$y=$ constant, etc.}$$ In many physics applications, particularly in thermodynamics (which is NOT the subject of this book), it is important to distinguish between partial derivatives with different variables held fixed. Make sure to discuss this, drawing lots of pictures, and introduce the physicists' notation of parentheses, with a subscript indicating the fixed variable. $$\left(\frac{\partial P}{\partial V}\right)_T \ne \left(\frac{\partial P}{\partial V}\right)_S $$