“Why do we have to learn this?” “When will I ever use this in real life?” If I had a dollar for every time I heard these questions, I’d be a rich woman. I love math, so I just figured everybody did. Well, I was wrong. Seven children and many math tears later, I realize that some people actually fear, abhor, and, yes, hate math. Yet, beyond the figures and calculations, there is a beauty. Answers for many difficult questions have their basis in mathematics. When my son loved his physics course (well, maybe love is a little strong) and voluntarily reads volumes by Stephen Hawking, and was still balking about learning higher-level math, I realized there was a little bit of disconnect. As author (and former aerospace engineer) William Flannery states, “The motivation for all mathematics beyond arithmetic is physics, and physics begins with differential equations. Yet in secondary school we are teaching complex algebra, geometry, and trigonometry before teaching the physics necessary to motivate their study.” Hallelujah! So he wrote these volumes (really lesson-a-day worksheets) so that children could learn calculus early, making it possible to study problems from physics and electronics that would motivate the entire math and science curriculum. This course is intended as a self-study course that any fourth grader with on-grade math skills should be able to succeed at. However, I think it would be almost more valued as a pre-calculus course for an older student -- ideally from sixth through ninth grade. It would certainly provide motivation and background for higher-level math and sciences in an easy-to-grasp way. What’s more, many concepts that will be introduced later in a standard math curriculum are previewed here. Even difficult concepts are made more understandable through this author’s incremental presentation and examples. No algebra, trigonometry, or geometry (beyond computing the area of a rectangle) are required to begin this course. The study is a pure study of calculus, the mathematics of change. The approach is gentle, incremental, and (dare I say it?) fun. Okay, maybe more like interesting if you really don’t enjoy math at all. What’s more, it is presented in real-life terms, using examples that kids can relate to and understand. Daily lessons are laid out on a double-sided 8½” x 14” page. Each begins with a presentation followed by an example and exercises. These are short lessons which should require less than 30 minutes each. The goal of the series is to teach the concepts of calculus in a way that students can relate to so they acquire a good intuitive grasp of the subject. This being the case, the author has tried to eliminate some of the laboriousness of the computations by using “easy” numbers where possible. Another very nice feature is that students work right in the book with plenty of workspace and all fill-in tables, graphs, etc. provided. The author has provided answers using a clever scheme that gives students help and confirms their correct answers, but prevents them from just “peeking.” Volume 1 is titled Constant Velocity Motion. Prerequisites are decimal arithmetic and a familiarity with rate problems, since differentiation and integration are just generalizations of variations of the familiar rate (velocity) * time = distance equation. It consists of 74 lessons divided into 5 units and lays the foundation for the course, introducing negative numbers, variables, functions, the distributive property, and (tah dah!) differentiation and integration! By the end of this first volume, your precocious pre-teen or pre-calculus student will know the basics of calculus and have solved more than a few differential equations on their own! The volume ends with an introduction to a very special differential equation -- one that launched modern science and mathematics - known as Newton’s Second Law of Motion, which is the theme of volume 2, Newton’s Apple. Expanding on the discoveries made in Volume 1, it begins with the realization that velocity is not generally a constant. In fact, a runner, car, or falling object will accelerate from its initial position. A ball thrown in the air will decelerate and fall back to earth. A hot wheels car will roll faster on linoleum than carpet. Many new concepts are introduced here, but incrementally and with ample explanation and example. There are 73 daily lessons again broken into 5 units. This volume ends by showing how calculus is used in electrical and electronic systems. Now that your student has differentiated linear functions (V1) and quadratic functions (V2), he/she is ready for polynomial and transcendental functions. According to Volume 3, these are Nature’s Favorite Functions. This third volume has 7 units and a whopping 96 lessons, covering a lot of ground including roots, radicals, exponentials, logarithms, trigonometric functions and second order systems -- again using practical applications to demonstrate the why of calculus. There is also an appendix which instructs you on the use of Freemat software (a freeware clone of the MATLAB programming language that engineers use) to work the CWT exercises. Lest any of this scare you off, there is also help via a Google.com discussion group for readers of CWT where your student can get answers to any questions that might arise. You can go to www.berkeleyscience.com to learn how to participate. If all of this is not sufficient, the author invites you to email him (address provided in book).

As I said before, I really loved the study of mathematics -- especially calculus. But I never realized its use and richness until perusing these books. Mine was a theoretical study. This book gives you all application. This is an answer to “When are we ever going to have to use this?” -- a great answer. This “study of change” could well transform your unmotivated mathematician into a rocket scientist (or an engineer, physicist, astronaut....).