Kalid Azad runs the website www.betterexplained.com. It’s is one of my favorite on the internet. The knowledge on this website should be implemented in every math program it the world. The articles on the site are the reason I bought Calculus Better Explained: A Guide to Lasting Intuition.
Azad takes complicated math concepts and explains them using analogy and real world examples. I’m an intelligent guy, above average in mathematics, and a physics major, but it wasn’t until I found Azad’s site that I truly understood Calculus.
After reading the articles on www.betterexplained.com, I understand what imaginary numbers and the number “e” represent. My trigonometric knowledge is intuitive and I know what the Fourier transform is accomplishing. The explanations on Azad’s website are why I bought Calculus Better Explained: A Guide to Lasting Intuition.
I thought I knew calculus. I took levels 1-3 and earned A’s in each class. This book showed me that while I knew how to do calculus, I didn’t know calculus. A physicist who doesn’t understand calculus is like a mechanic who can only change tires.
“The goal is to get Calculus in hours—not months—and have those insights stay with you.” This is the goal Azad states on the first page. Azad says that most of us are taught calculus by “ learning to build a car before driving it.” We learn calculus in the most difficult and unintuitive way possible.
It’s so difficult and obscure that we don’t even both getting to the good part of driving. Even if we do get to the driving part, we suck at it because we spent all this time learning how to build the car!
The main processes in calculus are derivation and integration. We learn the rules for this process, but many students do not understand the derivate beyond the power and chain rule. Also, most don’t grasp integration beyond “it’s the area underneath the curve.”
These explanations are correct, but they don’t develop mathematical intuition and knowledge. Azad explains these processes as “X-Ray Vision” and “Time Lapse Vision”, respectfully. This description sets the stage for how the book builds your working intuition of calculus.
Azad builds on these concepts by going over the entire function of calculus in each chapter, but increasing the level of detail each time. He first explains these concepts via an intuitive approach. Then he adds a natural description. Lastly, he adds the symbols that we are familiar with from class. By the time you see the derivative or integral symbol, you have a revised and intuitive understanding of what it’s asking.
The book won’t convert you into a math lover, but it will make you a much better mathematician. Potential STEM students give up not because of the science, but because of the math. Azad teaches the subject the way it’s meant to be learned. He teaches without complicated explanation and fun analogies involving pizza and trees.
I recommend this book to anyone taking or planning to take calculus. Pick it up Calculus Better Explained: A Guide to Lasting Intuition. Your inner mathematician will thank you.