You can learn calculus concepts starting from the formula distance = velocity * time.
Yes, that's true. That's what the book Calculus Without Tears is all about. It starts from the simple situation of a runner running with constant speed (velocity), and goes very step-by-step into actual calculus concepts, such as derivative, area under curve (integration), and differential equations.
The idea of the book is to make basic calculus concepts accessible to younger students, without need of much algebra.
Like I said earlier, calculus is the mathematics of change. It is usually studied as the last course in high school, or early in college studies. So should one study it earlier? I am sure people have varying opinions on that.
Certainly the aim of this book is NOT to further crowd the "mile wide" mathematics curriculum. But it provides something extra for gifted kids, or for students very interested in calculus and math (and physics). It also provides an alternative way to study calculus and can help students understand it better.
I enjoyed reading thru volumes 1 and 2. It is kind of a different approach, but can really make the student think and understand the concepts better. Too often, learning calculus becomes "mindless symbol manipulation" without much insight into what's happening.
Volume 1 of Calculus Without Tears concentrates on motion with constant velocity, modeling that with a function, graphing the situation, derivative in it (the velocity), area under a curve, and differential equations involved.
Volume 2 deals with the 'falling apple' - motion with constant acceleration, which is described by a quadratic function.
Volume 3 is about nature's favorite functions, such as polynomials, the exponential and trigonometric functions, roots and radicals.
So if you're curious, you can read my review, or go see the author William Flannery's site.
Tags: math, calculus, gifted
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