MadSci Network: Engineering |
Actually there are many uses, Bob! The particular application your question refers to is the mathematics of motion - most simply expressed as a one-dimensional (x-y) function of time. Acceleration, as you note, is just the derivative of the function for Velocity vs. Time. However in actual fact, velocity itself is really the derivative of the function for Position vs. Time. Thus, acceleration is in fact a second-order derivative, and rate of change of acceleration is third-order! Of course, this value can also change with time - it is in fact yet another function of the same 't' variable - and thus *its derivative* is yet another Time function: i.e., the rate of change of the rate of change of acceleration, which is actually the rate of change of the rate of change of position! :) "Higher order" derivatives like the above have a very wide variety of applications in the physical sciences: in fact, there's an important class of functions in physical science called the "analytic functions", which can be proven to be INFINITELY differentiable! (In other words, you cannot pick a finite number N such that the Nth derivative of any one of these analytic functions is NOT well-defined & continuous.) Probably the most common application of such functions is in "series approximations" (Tayler, MacLaurin, Laurent), which are often taught in calculus and basic analysis courses.
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