Although I won't stress the derivation of equations in this course, some of the derivations will be covered and an understanding of the derivations will assist in the use of the equations.
Differential calculus is involved with the study of rates of processes.
The calculus part comes in when we look at these processes in detail, that is, during small time intervals. That may be interesting in its self, but it doesn't give us any idea of the concentration between 0 and 24 hours, or after 24 hours. Using differential calculus we are able to develop equations to look at the process during the small time intervals that make up the total time interval of 0 to 24 hours. Then we can calculate concentrations at any time after the dose is given. In many cases the rate of elimination of a drug can be described as being dependent on or proportional to the amount of drug remaining to be eliminated.