Notes to accompany Chapters 12 to 16 of Stewart's Calculus - Early Transcendentals, 7th edition
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Notes to accompany Chapters 12 to 16 of Stewart's Calculus - Early Transcendentals, 7th edition

This repo is still a work-in-progress.



These notes were written to outline the major topics covered in Auburn University's Calculus III course based on Stewart's 7th Edition Calculus text. It progresses through most of the sections in Chapters 12 through 16, but Chapter 15 is reorganized slightly to introduce the Jacobian before introducing alternate coordinate systems. (In addition, sections 15.5 and 15.6 are omitted entirely to match Auburn's course syllabus.)

In addition, several original example problems based on these notes have also been written, which may be assigned as homework as an alternative to using problems from the text.

This project is based off of Steven Clontz's earlier HassNotes-10to14 project based on Hass's University Calculus, and a few notational conventions have been carried over from that project, such as using "σ" as the surface area parameter rather than "S".


The purpose of these notes is not to replace any calculus or analysis textbook, but rather to be used as a guide/outline for students and instructors covering the topics in a Calculus III course.

As such, when deemed necessary, mathematical rigor is abandoned for the sake of simplicity or brevity. (Many theorems only apply to "nice" functions, which usually assumes some level of continuity or differentiability.) Instructors are expected to elaborate during lecture whenever rigor is desired, but students should be able to use these notes as a "good-enough" resource for working on computational problems, particularly the included study problems.

About the Author

My name is Steven Clontz, and I'm a doctoral candidate in mathematics at Auburn University, and consider myself a bit of a hacker on the side. Feel free to check out my website at or my Github page


This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.

Please feel free to use and distribute the notes to anyone who is interested, but don't, say, bind them in a book and sell them without asking me first. :-)