Introduction

Welcome to the SageMath Calculus Tutorial! From initial concepts to increasingly complex techniques and applications, this tutorial is meant to accompany a high school- or college-level beginning calculus course. You'll learn how to interact with the incredibly robust, yet free and open-source, SageMath Computer Algebra System.

No previous experience with SageMath or calculus is necessary, though you will need to either download SageMath or work online at CoCalc in order to participate actively in the following lessons.

In particular, there are prepared versions of these lessons as executable worksheets right on CoCalc! First, create an account and a project. Then you can get a copy of the files from here!

If you know little or nothing about writing code - don't despair! Below most code snippets you will find a blue "Toggle Explanation" link, which when clicked will explain line-by-line how the code works. If you would first like to brush up on some pre-calculus and trigonometry concepts, this review may be of help. To bookmark a dynamic link to your last visited page, right click here: SageMath Calculus Tutorial - Last Visited, then select "Bookmark This Link" or your browser's equivalent.

If the tutorial's text is difficult to read, try zooming in or out using your browser's shortcuts. In Internet Explorer 7 and Firefox 1.0-3.x, pressing CTRL then + will zoom in, while pressing CTRL then - will zoom out. If your browser does not include such a feature, use the + and - keys to increase or decrease the font size from any page in the tutorial.

For any comments, suggestions, or questions, please write to Elliott Brossard, the author of this tutorial, at elliottb@u.washington.edu.

Contents

• Review
• Introduction
• Limits
• Continuity
• One-Sided Limits
• Limits at Infinity
• Supplement: Slant Asymptotes
• Tangent Lines
• The Definition of the Derivative
• Differentiability
• Differentiation Rules

Acknowledgements

A growing number of people have contributed their insight and advice to this tutorial. Not only does this give the tutorial greater polish; it encourages me, your author, to keep writing. Thank you!

• kcrisman, for being the first to give an in-depth critique.
• Harald Schilly, for providing HTML and JavaScript coding advice.
• Ron Ninnis, for suggesting and outlining a review on transformations.
• Minh Nguyen, for an invaluable and thoroughly detailed critique of the tutorial.
• My two sources of summer funding, the Mary Gates Endowment and the SageMath Foundation, for making this project possible.
• The SageMath development team, for giving students, teachers, professors, researchers, and engineers everywhere the means to conduct mathematics-related research and study in an extensible, free, and open-source environment.
• And finally you, my reader, for giving me an audience.