This is the homepage for the free book *Elementary Calculus*, by Michael
Corral (Schoolcraft College).

Latest version (2022-08-12): ElementaryCalculus.pdf

Current changelog: changelog.txt

Code samples from the book: code_samples.zip

Lab assignments: calc_labs.zip

Note: The PDF was built using TeXLive 2020 and Ghostscript 9.55 under
Linux (Fedora).

LaTeX source code:
calc12book-1.0-src.tar.gz

The book is distributed under the terms of the GNU Free Documentation License, Version 1.3.

You can buy a printed and bound paperback version of the book with grayscale graphics for $12.99 plus shipping at Lulu.com here.

This textbook covers calculus of a single variable, suitable for a year-long (or two-semester) course. Chapters 1-5 cover Calculus I, while Chapters 6-9 cover Calculus II. The book is designed for students who have completed courses in high-school algebra, geometry, and trigonometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but the old idea of an infinitesimal is resurrected, owing to its usefulness (especially in the sciences).

There are 943 exercises in the book, with answers and hints to selected exercises.

- The Derivative
- Introduction
- The Derivative: Limit Approach
- The Derivative: Infinitesimal Approach
- Derivatives of Sums, Products and Quotients
- The Chain Rule
- Higher Order Derivatives

- Derivatives of Common Functions
- Inverse Functions
- Trigonometric Functions and Their Inverses
- The Exponential and Natural Logarithm Functions
- General Exponential and Logarithmic Functions

- Topics in Differential Calculus
- Tangent Lines
- Limits: Formal Definition
- Continuity
- Implicit Differentiation
- Related Rates
- Differentials

- Applications of Derivatives
- Optimization
- Curve Sketching
- Numerical Approximation of Roots of Functions
- The Mean Value Theorem

- The Integral
- The Indefinite Integral
- The Definite Integral
- The Fundamental Theorem of Calculus
- Integration by Substitution
- Improper Integrals

- Methods of Integration
- Integration by Parts
- Trigonometric Integrals
- Trigonometric Substitutions
- Partial Fractions
- Miscellaneous Integration Methods
- Numerical Integration Methods

- Analytic Geometry and Plane Curves
- Ellipses
- Parabolas
- Hyperbolas
- Translations and Rotations
- Hyperbolic Functions
- Parametric Equations
- Polar Coordinates

- Applications of Integrals
- Area Between Curves
- Average Value of a Function
- Arc Length and Curvature
- Surfaces and Solids of Revolution
- Applications in Physics and Statistics

- Infinite Sequences and Series
- Sequences and Series
- Tests for Convergence
- Alternating Series
- Power Series
- Taylor's Series

- Appendix A: Answers and Hints to Selected Exercises

(2022-02-06) I fixed a font sizing issue with some subsection headers, due to a bad LaTeX font directive on my part, which was causing a slightly larger body font size than there should have been. Fixing that not only allowed me the opportunity to improve some wording I had been unhappy with, but the cumulative effect also resulted in both Appendix A and the GNU Free Documentation License section becoming 1 page shorter each. So the book is now 2 pages shorter with no loss of content! Big thanks to Tamás Zsoldos for finding that font issue, which I had never noticed.

(2021-02-23) After some (welcome and much appreciated) feedback I removed some of the more contentious commentary on other textbooks from the Preface. The original first draft of the Preface, fortunately, never saw the light of day. :) I might set up a page here to discuss more fully my views on calculus—in hindsight the Preface isn't the best place to do that.

(2021-02-20) The printed version on Lulu.com has been updated with the fixes from 2021-02-08. I just received the updated printed paperback version from Lulu today, and unfortunately TeXLive 2020 didn't fix the small compatibility issue that Lulu has when printing the book. The problem occurs only for a few TikZ decoration patterns, for example the figures on p.281: the diagonal line patterns are printed as solid blocks. The weird thing is that in the "print-ready" copy of the PDF that Lulu generated for me to review and accept, those patterns were still there and everything looked fine. So Lulu's printing system has a problem, and I will contact them about it. Overall it's not a big deal, as the number of figures affected is small (and doesn't hurt anything). It just looks nicer when the patterns are there. :) I have verified that this problem does not exist when printing the book on a "normal" laser printer, so I encourage people to print the book themselves if possible (local copy shops typically can do a spiral or other binding for a reasonable price).

(2021-02-08) I finally got around to updating the LaTeX source code to work with TeXLive 2020. This should make it easier for people to compile the book themselves, since the version I had been using (TeXLive 2011) is ancient. A typo was fixed as well. The printed version on Lulu.com is in the process of being updated; I'll post here when that is done (there is a new issue with compatibility).

(2021-01-19) I added some computer lab assignments to the Download section. These are modified from the assignments I gave when teaching Calculus I and II, with Schoolcraft-specific parts (e.g. file locations) removed. I tried to make the instructions as operating system agnostic as possible, but there are some Windows-isms left in (since the labs at Schoolcraft use Windows). The applications used are Gnuplot (for plotting), Octave (for numerical computation) and Maxima (for symbolic computation). Besides the PDF files I included the LaTeX source, in case anyone wants to modify the assignments to suit their needs.

(2021-01-04) I tried my best to improve this web page and perhaps make it slightly less hideous and disorganized. I also added a zip file with the code samples in the book.

(2021-01-01) Added a link for buying a paperback version of the book on Lulu.com. The price is $12.99, which covers the cost of printing and binding. No color graphics, though, except for the cover (which Lulu's template insisted on altering). If there is demand for the full color version (as in the PDF) then I might set that up through Lulu as well.

(2020-12-31) The full version (1.0) is finally available! Chapters 1-5 cover Calculus I, while Chapters 6-9 cover Calculus II. I wanted to finish the book by the end of the year, and I managed to get it in on the very last day of the year. :) For now I just wanted to get the book out, but I will try to fix up the web site so that it doesn't look like a 1992 time warp. :) That will be my next project.

(2020-08-04) Five more exercises were added, bringing the total to 475 in the new 0.5b release. Some wordiness was reduced to make room for the extra exercises, while keeping the page total the same. See the changelog for all the changes. I am now up to Section 7.3 (Hyperbolas) in the second half of the book, and am still on track to finish by the end of the year.

(2020-06-03) I decided to move the material on Improper Integrals to Section 5.5, since that will mirror the finished book. I moved the old Section 5.5 (Average Value of a Function) to what will be Chapter 8. With the change in content for Section 5.5, there are now 470 exercises (up from 461) in the new 0.5a release. Progress on the second half of the book is continuing at a good pace.

(2020-05-27) The first half of the book has been fixed up quite a bit and is now complete; there are now 461 exercises (up from 428). It is released as version 0.5, while the older version has been renumbered to version 0.1 and removed from the site. Work on the second half of the book is continuing. Thanks to the pandemic lockdown here in Michigan I am more focused on the book and remotivated to finish it this year. Stay tuned.

(2020-05-17) Progress has resumed on the book, after too many years of inactivity (life...really). I am in the process of revamping the first 5 chapters with a lot of improvements, typo fixes, corrections, and incorporation of feedback (thanks to the people who have emailed me). I am now up to Section 4.3 (Numerical methods), whose initial state was unsatisfactory. I will expand Section 4.4 (Mean Value Theorem), continue on with Chapter 5, then start the Calculus II part. I will provide periodic updates.

(2016-01-24) Initial version 0.1 is released.