Everyday Calculus: Discovering the Hidden Math All Around Us

Sneaky Intro to Differential Equations

The systems, events and measurements highlighted in this fine little book are the "everyday" part-- the calculus is not! In order to model the types of everyday experiences the author describes in fine fashion, simply taking the first or second derivative to find slope or acceleration doesn't do much. The truth is that he's subtly talking about dynamical systems-- differential EQUATIONS, not just calc as we'd see it as an isolated technique. The real physics, engineering, biology, etc. that these equations model require matrix vectors and really advanced concepts and techniques, many of them not even able to be generalized beyond that model or problem. In fact, of the four methods used in dynamical systems (analytic, qualitative, numeric and the newest family member stochastic/statistical), most are incapable of modeling anything but the simplest versions of the underlying "reality." We can't, for example, specify the design of an airplane wing analytically, so we use qualitative (graphs, for example) and numeric ("guesses" with computer algorithms), which as we engineers would say, gets us "close enough." I just didn't want you misled into thinking that the calculus itself was everyday or simple. The author does a wonderful job of hand holding us through the foundations. There is a lot of value in this in: 1. Getting us "ready" for advanced applications 2. Giving us a fun glimpse at why calc is so important 3. Giving us an intuitive feel for why we model in the more advanced form. Every High School student interested in math should read this, even though the true topics are advanced undergrad and grad level! The author actually makes this possible, which is a rare feat. If you're an AP math student, you'll get this easily, and the appendix will transition you to undergrad. The sneaky part is that the solutions to the calculus described here are quantities, whereas the real-life modeling dynamical systems equations have functions as solutions. This is normally no...