# Review of "Everyday Calculus" by Oscar Fernandez

## Everyday Calculus, Discovering the hidden math all around us by Oscar E. Fernandez.

"Everyday Calculus: Discovering the hidden math all around us" by Oscar E. Fernandez, ISBN 978-0691157559

This book is enjoyable, lively and short. It also has wrong title. A much better title would be "Single day calculus", because the entire book describes one day in author's life. Of course this day is filled with mathematics, in particular by calculus. The mathematics starts at night with sleep cycles (periodic functions), then continues in the morning on TV with a little of CNBC channel watching, (price changes and derivatives), then planning for retirement (exponential growth), etc. Even mundane events, like filling coffee mug at Starbucks a full of formulas!

The major theme underlying the book is change in one variable produces second variable. Change in position (distance traveled over time) is called velocity. Change in velocity is acceleration. Calculus is study of these dependencies, thus it is study of change. During a course of a single day we experience lots of changes: position, velocity, volumes, financial assets. By using derivatives and integration we can relate any pair of variables in our life.

Compared to my previous reading on mathematics (The Grapes of Math and How Not To Be Wrong), this book is much shorter, does not provide much historical context, instead focusing on specific formulas that describe immediate physical entities. My favorite description was how catching speeding cameras on a stretch of highway is related to the Mean Value Theorem. In essence, if we notice a car driving 60 mph at the start of 1 mile road stretch, then 30 seconds later still driving 60 mph at the end of this road stretch, we can safely say that at some point during this 1 mile the car was traveling 120 mph (1 mile / 1/120 hour)! The beauty is that we do not even know the maximum speed, just that it must have achieved at least 120.

I highly recommend this book to anyone interested in popular mathematics, and to any high school kid who asks a parent or teacher "Where am I going to use this math?" The answer is "everywhere".