Thinking About Equations: A Practical Guide For... May 2026

Using units to catch errors or even predict the form of a solution.

Checking if an equation makes sense at extremes (e.g., zero or infinity). Thinking About Equations: A Practical Guide for...

Rather than teaching new complex math, it teaches how to apply basic tools (calculus and introductory physics) to gain deeper insight. Using units to catch errors or even predict

Using visual and geometric properties to simplify problems. Using visual and geometric properties to simplify problems

Using "Fermi questions" and simple physics to get ballpark figures.

, written by Matt A. Bernstein and William A. Friedman, is a supplement designed to bridge the gap between rote mathematical manipulation and physical understanding. Core Premise

The book aims to help students move beyond just solving for a variable and instead learn to "interrogate" an equation. It provides a "toolbox" of techniques—reminiscent of Richard Feynman's famous "different box of tools"—to analyze, simplify, and verify mathematical expressions in a physical context.