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:

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.

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.

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.

Check back for updates periodically.

- 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.

- 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.
- 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.
- 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.

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

- Front Matter: title page, preface, table of contents. Thanks to Dr. Michael Green for advice on "toning down" my criticisms of well-established approaches to Calculus texts and instruction. 168,289 bytes.
- Chapter 1: Symbolic Logic. Was fairly complete, but got to be too large. I am revising and cutting it extensively, informed by some experience from using it in my classes. I do want students to see the quantifiers, since we use them in epsilon-delta definitions and proofs. Set theory stuff remains, though not as sophisticated as it was at the start of this project. 588,180 bytes.
- Chapter 2: Real Numbers, Algebra and Functions. Getting more complete, but probably needing revision. I am trying to have the reader revisit algebra and functions in a different and sophisticated way, to encourage him (or her, I use it with "gender-neutral" intent) to think more rather than just "go through the motions." You can have a look at my latest, and probalby last, attempts to diagram functions to help students visualize complicated functions as multistage processes, or "machines." If there's a better system of doing so out there, let me know! 2,248,287 bytes.
- Chapter 3: Limits and Continuity.
This started with the standard treatment, and then it just
occured to me that there are better ways, so it got a major
overhaul, probably around 2003, and has stayed in the same
spirit ever since. My students find it hard but they ask
much more sophisticated limit questions than before. I
concentrate heavily on "forms," both determinate and
indeterminate. Except for the sequence sections I'm
still mulling whether to include, I have used this
in courses three times. Even my best students think this is
hard, so I must be doing something right! Limits
**are**hard, but after this they should be able to hand-wave more of the kind of limits you get with wacky improper integrals and ratio/root tests. 1,208,453 bytes. - Chapter 4: Computing derivatives.
Fairly complete, but I want to sneak in more graphing so
I don't have to make a big deal about it in a single section
later. I am very big on Leibniz notation! I am presently needing
more and revised exercises. Note that I do ALL differentiation
rules, with the exception of hyperbolic functions, here. So the
logs, exponentials, arc-trig's and
*(f(x))*(check out my explanation for a general formula for that derivative!) are all done here.^{g(x)}Hardly any applications are included yet, though I will include more graphing problems within the text here. The purists will note that I do graphing before the Mean Value Theorem, so I let students play with increasing/decreasing before I prove

*f '*>0 implies*f*increasing, for instance. This is done for pedagogical reasons. It seems intuitive enough, and the proof can occur later when the fact is well-learned. I still have to find a way to work second derivatives into the text better. The next chapter will include the MVT, its applications, and the other usual applications, including more graphing, when all is done. 1,523,632 bytes. - Chapter 5: Analyzing
Functions with Derivatives.
Still in infancy. Here I do get to use the logic more, since the
statements, proofs and applications of theorems are often require
logically equivalent forms of the basic results.
One thing we plan to have different about the approach is that we will mix some graphing problems in with Chapters 3 and 4, so that we do not have to have omnibus sections of this chapter devoted to graphing. Graphs reflecting the sign of

*f '(x)*do not have to wait until this chapter, though the proof that positive derivative means increasing function will be done here. This will have related rates, MVT applications (*f '*in some range, what is the range in which we can find*f*given a starting point?), max/min problems, etc. For now, don't expect much here. 872,372 bytes. - Chapter 6:
Basic Integration. Still in alpha stage, if that. The usual
stuff at the moment. One plan is to show why the Fundamental Theorem
is more obvious, by exploring position/velocity.
At the moment there is an "artifact" hyperbolic section, that is just beginning, and likely to end up somewhere else.

One key here is that we are

**very careful**in choosing the method for substitution. The short-cut, completing-the-chain-rule-derivative method is avoided here because it is a dead end, and nearly useless for advanced methods of the next chapter. Why authors continue to advance this as the method to use here is beyond me. Instead, our method here (and of course we're not claiming to have invented this but that we're choosing this method) is to replace everything in the original integral with*u*and*du*terms. We show the reader the other methods but focus on the method we believe has more use in their future studies, such as trigonometric and "miscellaneous" substitution.See also notes on the next two chapters. 800,431 bytes.

- Chapter 7: Advanced Integration Techniques.
This has had some good update in the last few years because I taught the course, and freshened up this chapter, which was already pretty well developed. I'm maybe 7/8-finished here with the examples and explanations. Parts, partial fractions and trig integrals just need polishing and problems. Trig substitution is a new section that has seen some improvement over the recent years but should probably be augmented. And they all need more problems! Tables and other techniques not yet begun. Also some techniques for more general, uglier rational integrands in the spirit of Edwards & Penney will hopefully appear here. 557,943 bytes.

- Chapter 8: Applications of Definite Integrals.
Barely started (less than two pages!) It has definitely been
on the back burner awaiting inspiration.
After consulting with respected colleagues, I finalized (I think) the decision to keep this chapter placed

**after**the advanced integration techniques, presently Chapter 7. My one-time chairman Dr. Gerard East in particular made the case that students just don't get enough integration practice immediately after the advanced techniques until multivariable stuff or differential equations otherwise. Presently 62,145 bytes - Chapter 9: Advanced Limit Techniques and Improper Integrals: This got a big boost from my Calc 2 courses in Spring 2008 and 2009. I had put it aside for years, but once I got started it really was kind of fun, particularly using PSTricks to shade under curves for improper integrals. 613,442 bytes.
- Chapter 10: Series of Constants.
This also got a boost from my Spring 2008 and 2009 Calc 2 courses.
I'm not 100% sure that I will follow the usual outline. Many professors have indicated they would like to see power series earlier, and later worry about convergence in that context. I may experiment to see if this and Chapter 12 can be consolidated in a respectable manner.

But so far I seem to be following the standard outline, more or less. 453,511 bytes.

- Chapter 11: Taylor polynomial/series
stuff.
This has been given a preliminary overhaul, with the original
(plodding) introduction replaced with a summary of what
will be developed and why we should care, an early introduction
of Taylor Polynomials followed by a shorter (truncated)
development from first principles, then the usual stuff,
plus a section which discusses when things go wrong:
with piecewise-defined functions, and functions where the
singularity doesn't lie on the real line, but is found
in the complex plane. There is some introduction to
complex variables, hopefully just enough to whet the
appetite but not enough to scare anyone away from them.
I will (soon?) make another pass over this chapter since this major overhaul to be sure it works the way I want it to. 817,070 bytes.

- Chapter 12.
I thought I'd at least get started
on some analytic geometry, inluding vectors and
polar/cylindrical/spherical coordinates. I got a few
more pages written but it's still in its infancy.
I also included the "layout" pages for any LaTeX folks
who are wondering. I should point out that, at the
time anyhow, it seemed simpler to just fool the
program into thinking I wanted A4 paper, so it wouldn't
complain so much when I wanted to use more of the page.
If I recall correctly, I was using an original
print of Angus Taylor's
*General Theory of Functions and Integration*to figure out the dimensions I wanted. I've been told by folks who know better that my lines of text may be a bit long, and I may need another approach, though I'm not sure what. I don't like how most calculus texts leave wide margins for occasional figures, which means a lot of wasted space. I'm finding out that the LaTeX figures in the book class do too (waste space), so I'm trying to minimize that. Anyhow, this last file is 927,475 bytes, which is up quite a bit from last time I updated all the chapter links, so I must have done something in the meantime.

Michael M. Dougherty, with home page here.