A Tutorial Guide to Calculus

This is an online calculus textbook, written in tutorial style. Numerous examples are worked out in detail, step-by-step, and fully explained in plain language. The content is suitable for a high-school student who doesn’t yet know anything about calculus, and would like to learn what it’s all about. A strong foundation in high-school algebra and functions is assumed. The chapter on limits takes students from zero knowledge up to a facility with using the precise definition of limit, in about 200 pages.

Click on any of the links in the table of contents to access the content. As of May 2021 it’s very unlikely that I will be posting anything additional content on this page for a while, as my current focus is working on the linear algebra content, and then on the success at university content, the physics content, and the logic content. I plan to return to posting more calculus content sometime in 2022.

Table of Contents


Introduction: What is Calculus?

Chapter 1: Prerequisites

Chapter 2: Limits

Chapter 3: Rules for Differentiation

Chapter 4: Applications of Differentiation

Chapter 5: Introduction to Integration