This is the homepage for the free book *Elementary Calculus*, by Michael Corral
(Schoolcraft College). If you are looking for the *Vector Calculus* homepage, go
here.

For now, **only the first part of the book**, covering Calculus I
(i.e. first-semester calculus), is available.
I am still working on the second part of the book (Calculus II), which I hope to have done by Fall 2016. For now,
at least, you can get an idea of the approach that the book takes. This is a preliminary version, so there could possibly be
changes, though I don't anticipate any major change. When complete, the book will have 10 chapters. The first part
contains Chapters 1-5 and has 428 exercises; it is suitable for a first-semester course in the subject.

I omitted the preface from this first part of the book; it will be in the completed book. In the meantime I will add some notes here concerning the reasons for making the book, including some opinions on the current state of calculus and the way it is taught. I think I need to update the entire design of this site to make these types of discussions easier. So keep checking back here!

You can download the latest version (2016-01-24) of the first part of the
book *Elementary Calculus* here: calc12book-part1.pdf

Current changelog: changelog.txt

The book is a PDF file, which requires a PDF viewer such as the freely available Adobe Acrobat Reader or noncommercial software (e.g. Evince, Okular, xpdf) to view it. The book is distributed under the terms of the GNU Free Documentation License, Version 1.3.

For those who want to view and/or compile the book's source files, the LaTeX source code is available here:
calc12book-part1-1.0-src.tar.gz

You will need a relatively recent LaTeX installation to compile the source code. In particular, you will need
a recent version of the TikZ graphics package (at least version 2.0), which is available as part of
the TeX Live system, or you can get it here:
http://www.texample.net/tikz/builds/.
A build script (calc12book.sh) for Linux/UNIX systems is included for building the PDF file.

**Book description**: This is the first part (Calculus I) of
a text on elementary calculus, 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 infinitesimals
is resurrected, owing to its usefulness (especially in the sciences).

There are 428 exercises in this first part of 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
- The Exponential Function and Natural Logarithm Function
- General Exponential and Logarithmic Functions

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

- Applications of Derivatives
- Optimization and the Second Derivative Test
- 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
- Average Value of a Function

- Appendix A: Answers and Hints to Selected Exercises
- GNU Free Documentation License
- History
- Index

**News**

(2016-01-24) Initial version 1.0 is released.

**Contact**

The author of the book, Michael Corral, can be reached via email at

*Last updated: January 24, 2016*