Introduction to total differentials and measuring how changes to one or more independent variables effect a function of those variables.

Example provided to demonstrate the structure of a total differential. $dU=\left(\frac{\partial U}{\partial x_1}\right)_{x_2} dx_1 + \left(\frac{\partial U}{\partial x_2}\right)_{x_1} dx_2$

Review of both scalar and vector forms of infinitesimals relating the example just presented to $d \vec{r}$

Description of ratios of differences while clarifying that a derivative is NOT a ratio of two differentials since it matters what is held fixed.