The derivative is introduced as an instantaneous rate of change and it is shown how this can be determined from first principles. Techniques (sum, product, quotient and composite function rules) are then explained and the connection with small changes is illustrated. Economic interpretations via marginals are given.

Looking at the Korean and Vietnam Wars, we evaluate the influence of casualties disaggregated by space/hometowns and time on mass opinion in both the Korean and Vietnam wars and on individual opinion in the Vietnam War. We find a powerful connection between US casualties and public support for a war consistent with our expectations about the importance of casualty trends, the geographic locations of casualty hometowns, and the interaction of these dynamics. Disaggregated casualties are better able to capture variation in mass public and individual wartime opinion than are logged cumulative national casualties – the standard wartime measure employed. We also find that the wartime information-opinion process operates more strongly in the ex ante identifiable early stages of a conflict, and less effectively later in a conflict when casualty expectations (and thus the value of new information) begin to harden. These results strongly support the general notion that casualty patterns act as an observable proxy for our RP/ETC process by capturing information that individuals draw on to generate ETC and formulate wartime positions, improving our ability to understand and predict wartime opinion.