I started writing this book as a junior in high school in my second semester of AP Calculus BC with the goal of writing a textbook from the perspective of a student so that better analogies could be made to increase understanding, since I remember what it was like not long ago to not understand.

Calculus is the mathematical study of change. In this text, we outline the basics of the three main subjects of calculus: Differential Calculus (Calculus I), Integral & Series Calculus (Calculus II), and Multivariable & Vector Calculus (Calculus III). We attempt to do this in a fluid and intuitive manner that is easy for those of various mathematical backgrounds to understand. This book is intended as an introductory text to calculus and is best used when supplemented with lectures on the main topics of each chapter.

At the end of each chapter, following the chapter summary, there will be exercises split up by which section of the chapter they should be assigned with. Solutions to odd-numbered exercises will be provided at the end of the book. Also at the end of the book will be some of the more involved derivations of different derivative and integral rules, like the chain rule, derivatives of inverse trig functions, and more.

This textbook is very much a work in progress. In its current stage, no formatting has been finalized (in fact, in most areas, it will be changed). Exercises will be added in future versions. After the three current developed sections are completely finished (barring formatting and possibly exercises), up next will be chapters 3, then 5, and then 6, to finish off the Calculus I section of the book. Rough drafts for chapters 3 and 5 are complete, and chapter 6's rough draft is about halfway done. Suggestions and corrections are welcome and encouraged, both of current content and suggestions for future content (examples, exercises, formatting tips, etc.). You can contact me here.

Calculus (v1) (1/29/2026)