Introduction.sagews

Introduction

Welcome to the SageMathCloud 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. No previous experience with SageMath or calculus is necessary. If you would first like to brush up on some pre-calculus and trigonometry concepts, this review may be of help.

For any comments, suggestions, or questions, please write to Cody Ryu, the custodian of this tutorial, at [email protected].

Contents

• Review

• Introduction

• Limits

• Continuity

• One-Sided Limits

• Limits at Infinity

• Supplement: Slant Asymptotes

• Tangent Lines

• The Definition of the Derivative

• Differentiability

• The Rules of Differentiation

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!

• Elliott Brossard, for creating the SageMath Calculus tutorial, from which this document is derived.

• 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.

• Elliot Brossard's 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.