The Complete Physics Companion

The advanced, calculus-based companion to The Complete Physics Crash Course

Introduction: Why This Book Exists

Most physics courses hand you a formula, tell you to plug in numbers, and move on. That approach gets you through an exam, but it leaves the formula feeling like a magic spell instead of a discovered fact. This book takes the opposite approach. Every law of physics in these pages is derived — built up from a smaller set of assumptions using the tools of calculus, so that by the end you understand not just what the equation says but why it has to be true.

This is the advanced, calculus-aware edition. It assumes you are comfortable with single-variable differentiation and integration (derivatives of polynomials, exponentials, and trig functions; definite and indefinite integrals; the idea of a separable differential equation) and with basic vectors and trigonometry. If calculus is new to you, this is the wrong place to start — go work through The Complete Physics Crash Course first, the algebra-based companion volume that covers the same physical world without derivatives or integrals, then come back here once the notation feels familiar. Nothing here is harder physics than the Crash Course; it is the same physics, argued from first principles instead of asserted.

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