The current mathematics publishing paradigm produces quality textbooks with significant shortcomings. One considerable issue is that they are large, yet static; one generally chooses a book based on its strengths acknowledging that you must put up with its shortcomings. Other common issues relate to the inappropriate "new edition" update cycle and the cost.
The open textbook movement seeks to address some of these shortcomings by offering flexible, low-cost alternatives. The source files for these texts are open under generous copyright restrictions; you may edit a text to suit your purposes. The update cycle is geared towards fixing mistakes and adding valuable content, not making profits.
Authoring an open textbook is no small feat. It requires a great amount of time to write, and even then, a quality product is not ensured. Authors benefit greatly from professional editors, professional graphic artists, plus the feedback that comes from paying colleagues to review a text before it goes to publication.
The APEX model for writing textbooks provides a solution to the above problems. Authors collaborate on a text; all parts of the text writing process is handled by a variety of like-minded people so that the individual time/resource commitment is reduced to manageable levels. Some write the text; others write exercises; others produce graphics; some edit, ensuring the text has "one voice"; others write helpful LaTeX (or other suitable software) macros; others review.
The APEX model for writing texts was developed here at VMI as some of the faculty considered writing texts but balked at the time commitments necessary. So far, three texts have been produced (see links below). The matrix algebra and MATLAB/Mathcad texts were produced first and are not "true APEX" texts. Each was written primarily by one author, with a little collaboration from others. However, in the Fall of 2011, VMI awarded Lt. Col. Gregory Hartman a Jackson-Hope New Directions in Teaching and Research grant, providing him course releases so he could collaboratively write a Calculus text. A text covering "Calc I" through "Calc III" has been written and is the text used in our Calculus courses. While the primary author is Lt. Col. Hartman, three other authors have contributed and another colleague has provided editing.
- Fundamentals of Matrix Algebra 3rd Edition, by Gregory Hartman. A college (or advanced high school) level text dealing with the basic principles of matrix and linear algebra. It covers solving systems of linear equations, matrix arithmetic, the determinant, eigenvalues, and linear transformations. Numerous examples are given within the easy to read text. This is currently the text of MA 103, Matrix Algebra
- An Introduction to MATLAB and Mathcad, by Troy Siemers. This textbook, or really a “coursebook” for a college freshman-level class, provides an introduction to programming and problem solving using both MATLAB and Mathcad. We provide a balanced selection of introductory exercises and real-world problems (i.e. no “contrived” problems). We include many examples and screenshots to guide the reader. We assume no prior knowledge of Matlab or Mathcad.
- Calculus (version 2.0), by Gregory Hartman et al. A college level treatment of standard Calculus topics beginning with limits and ending with iterated (multivariable) integration. The material is presented in a "traditional format," designed to make the transition from popular Calculus books (such as Stewart or Thomas/Finney) straightforward. This text is suitable for most "Calc I," "Calc II" and "Calc III" courses. This text is currently in use in MA 123, 124 and 215, Calculus and Analytic Geometry I, II & III at VMI. The source files can be found at github.com/APEXCalculus. The entire text can be purchased in three volumes from Amazon.com ($11 each); search for APEX Calculus. There are older versions available; the latest is version 2.0. More information can be found at www.apexcalculus.com.
- "Calculus 1" covers limits, derivatives, applications of derivatives and the basics of integration; Chapters 1 - 6.1.
- "Calculus 2" covers integration, including methods and applications, along with sequences and series; Chapters 5 - 8.
- "Calculus 3" covers parametric and polar equations, vector valued functions, and multivariable functions; Chapters 9 - 13.
Below are links to pdf's of each of the above volumes. The color versions look nicer, though the black & white versions are better suited for printing (the texts from Amazon.com are black & white to reduce cost).
- Calculus 1: This covers limits, derivatives, and an introduction to integration. (Used in MA 123)
- Calculus 2: This covers integration, techniques and applications of integration, sequences and series. (Used in MA 124)
- Calculus 3: This covers conic sections, parametric equations, polar coordinates & functions, vectors and vector-valued functions, and multivariable functions, including partial derivatives and iterated integration. (Used in MA 215)
- Calculus (all chapters)
- The source files are found at github.com/APEXCalculus. The text is covered by the Creative Commons Attribution-Noncommercial 3.0 license, so you can feel free to modify the contents and redistribute. If you do so, please acknowledge our authors and do not seek to make money off of our work. To get the whole Calculus book, run the file Calculus.tex; Calc I is created with CalculusI.tex, etc. Running these .tex files is probably not for the faint of heart; they are designed to run under XeLaTeX using the Calibri font. If you have interest in working with the authors clean up the TeX code, please contact us.