Dr. Michael Dougherty's Calculus Textbook Project

This page contains excerpts from my calculus textbook project, written in collaboration with John Gieringer of Alvernia University, Reading, Pennsylvania. It can be downloaded in its entirety (9,662,820 bytes, updated November 20, 2012) here:

First Year Calculus for Students of Mathematics and Related Disciplines (PDF File)

written in collaboration with John Gieringer of Alvernia University, Reading, Pennsylvania. The "big file" above will always be the most recent available version. Older versions of the individual chapters are given below, for smaller downloads. Those files may be very old! (OK, I updated them November 20, 2012.)

Advice for Other Authors

If you are intersted in using your own textbook manuscript in your classroom, I have some advice for you. For a little paper on my own personal experiences, check out Teaching from Your Textbook Manuscript. While much of it probably seems obvious enough, one strategy which worked especially well for me was to have students turn in "binders" for grades, collated by topic. So for my Section 1.1, they would first have the pages from my textbook project (2-sided, pre-punched), then my classroom notes in their own hands, then the graded homework and possibly quizzes. Next would be the same for Section 1.2, and so on, until it was time for an exam. They turned in their binders the day they took the exam, and when the exam was returned they were expected to put it into the binder after all sections it covered, along with the key. Then it would all start over again. This really helped them to see how to organize things. In fact by the end of the semester many had two or three different binders because it piled up so much, but being organized as it was, on the second (or so) time through it made for an easy read.

As simple as it sounds, I had many students tell me they started doing it in their other courses, even though it was not required, and how amazed they were how effective it was to help them study. Before I had them do this for a grade, they had the handouts scattered throughout their "stuff," causing predictable problems.

The paper above describes more of the hows and whys of teaching from your own book. Maybe there's something interesting and useful to be found in the paper. I sure enjoyed writing it and presenting it at an MAA sectional conference.

All Web Updates of the Book are Frozen Until Further Notice

This project is getting closer to completion, and we are hoping to work harder on a publishable form, and for copyright reasons it might not appear here when completed. Also, there are some new innovations, and admittedly we don't want to give away any more of the store before publication.

Also some courses are classroom-testing it in its present form, and it could goof them up if we keep changing the content.

A big thank you and shout-out to Professor Sarah Koskie of IUPUI for some suggestions for improvement, and for "field-testing" some of the material in one of her classes.

Section 5.1 has had a lot of changes and additions. It's close to complete. We introduce higher-order derivatives, explain the meaning of f'', and immediately set off to graphing. Most professors would probably want to make it a two-lecture section.

Chapter 11 had lots of changes. A few minor tweaks will happen in the next day or so but otherwise it will be frozen for a while.

Chapter 5 is now on the editing block.

What's Different?

Our textbook is meant to be read--curled up with and read! We go into much detail, with more examples than most in the topics which are the most confusing. If you currently are using one of the standard textbooks, you can use ours as a supplement. If you want to learn calculus on your own, ours can be your main text (though the standard ones have more exercises). We occasionally hear from folks around the world who happened upon this site that they found it useful, and we hope you agree.

A few "differences" might turn off some readers, particularly regarding the first two chapters. We spend a chapter on symbolic logic so we can use it elsewhere, including a rather in-depth (for a calculus book) development of epsilon-delta proofs. If you just want more complete examples for derivative and integral problems, you can go to those sections (preferably from the current "whole book" file linked above). If you want a much deeper, and more useful and "form-based" discussion of limits (to better prepare students for things like convergence tests and improper integrals), check those out.

Another difference is that there is a very expanded Chapter 2, which is still preliminary but has some good algebraic stuff which is easier to accomplish after raising the sophistication level, made possible by a study of Chapter 1's logic.

While this is a work in progress, some chapters and more sections are basically complete and have been successfully used in courses. We're hoping this is the year we can really push it towards completion.


If you have any comments please send them to michael.dougherty@swosu.edu. If you found this material useful, we would like to know. You are free to use this pre-published material in your classes or for your own studying, but if you use printed versions we would appreciate credit, and you letting us know. We are most encouraged to work longer hours to complete the book when we hear from readers who found it useful. If we are doing something wrong we'd like to know that too.

Check back for updates periodically.

Most Recent Changes

John Gieringer (of Alvernia College in Reading, Pennsylvania) is the second half of the "we" and "us" mentioned above, and has contributed many and varied fine examples, and caught numerous mistakes, and made the original author need to learn to better draw circuits! (Thanks a lot, John, ;-)) These are spread all over the first five chapters.

More on why this book is different

In case you're wondering why this book is different, here are a few quick reasons.
  1. You can read this book just by reading this book, mostly without a large pad of paper and a lot of pens next to you trying to figure out why what we wrote is true, or for that matter what was meant. At least that's the goal: a book you can relax with to read calculus!

    Well, that's not quite right. You can, for the most part, read the book without a lot of frustration because it's spelled out for you in more detail than usual, though it never hurts to have that paper and pen ready to clarify things for yourself. And of course, exercises are included (not enough yet but getting there) and those are usually nontrivial, requiring a creative effort and lots of paper on the part of the reader if the material is to be truly learned.

    The usual technique for a calculus book is the opposite, arguably leaving out too much detail--or trying to pack too much into each of the (consequently) insufficiently numerous examples--and thus requiring the student to mull over points for a very long, frustrating time. That's OK and time-tested, particularly for students who have the time and energy to work through the explanations and exercises, often with the help of an instructor or teaching assistant. However, students who don't have the tolerance for incomplete explanations but who might make fine students if more is spelled out for them might find a resource that fits them better here. Furthermore, even the former group of students often leave calculus with some glaring misconceptions despite their persistence, and a more expository presentation should benefit them as well.

  2. There is much experimentation with topics and orders, though if it is important enough for most calculus texts, it will be here too, eventually anyhow.
  3. The whole project is done in "black and white," with no color illustrations, though plenty of figures are included. Well, actually one colored graphic was stolen from Wikipedia. There are no margin notes (though we make liberal use of footnotes), and we only use multicolumns in exercises and when it can save a tremendous amount of space, or when a small figure or group of equations can be wrapped by the explanation.
  4. You can have these beta versions for free! In fact, if you are an instructor and have any use for anything here, feel free to print it up and distribute it, as long as you (a) do not profit from it (through, for instance, sales), (b) give us credit, and (c) don't try to include it in anything you're writing without first asking us and of course giving us credit. We'd be very pleased if any of our ideas here are helpful to anyone, and we'll be the first to give our permission for that. While we do hope it will eventually make it into hardback print, which we intend to be much cheaper than present offerings, we don't mind a bit of free advertising. In fact, if you have any ideas to share we'll put them in there and give you credit, assuming we like them too, and they seem to be an appropriate fit.
Special Thank-Yous (Michael Dougherty): I have had a couple of people send me edits that I have not had time to incorporate. I have them saved though, and will include you in my acknowledgments when the time comes. If you've sent me feedback regarding this project, this means you.

Note that the text is first formatted in LaTeX, which generates a DVI file, which is then converted to Postscript, and then to PDF with ps2pdf. A good program for rendering the PDF files for the screen is Adobe's Acrobat Reader (see link at bottom), though there are others, particularly gv and evince for Linux.

Graphics are handled almost entirely through the PSTricks package under LaTeX. Thanks so much to that community, particularly Herbert Voss for all the great work done on Timothy Van Zandt's original PSTricks package. See also notes at the bottom of the Chapter 12 commentary, at the bottom of this page. --MMD

Individual chapters, current as of November 20, 2012 (see top link for whole book as of that date)

Please note that all book pages are copyright Michael M. Dougherty.
Michael M. Dougherty, with home page here.