A full course in differential equations involves application of derivatives to be studied after two or three semester course in calculus. A devirative is the rate of change of one quantity with respect to another;
for example:the rate at which an object’s velocity changes with respect to time (compare to slope). Such rates of change show up frequently in everyday life. For example, the compound interest law states that the velocity of interest accumulation is proportional to the principal account value, given by dV(t)/dt=rV(t) and V(0)=P, where P is the initial (principal) account value, V(t), a function of time, is the current account value (on which interest is continuously assessed), and r is the interest rate (dt is an instantaneous time interval, dV(t) is the infinitesimal amount by which V(t) changes in this time, and their quotient is the accumulation rate). Although credit card interest is typically compounded daily and described by the APR,annual percentage rate, this differential equation can be solved to give the continuous solution V(t) = Pe^(rt). This article will show you how to solve types of differential equations commonly encountered, especially in mechanics and physics.
