APEX Calculus

Thank you for reading this short preface. Allow us to share a few key points about the text so that you may better understand what you will find beyond this page.

This text comprises a three—volume series on Calculus. The first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6.1. The second text covers material often taught in “Calc 2:” integration and its applications, including an introduction to differential equations, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 5 through 8. The third text covers topics common in “Calc 3” or “multivariable calc:” parametric equations, polar coordinates, vector-valued functions, and functions of more than one variable, found in Chapters 10 through 15. All three are available separately for free at apexcalculus.com¹, and HTML versions of the book can be found at opentext.uleth.ca².

These three texts are intended to work together and make one cohesive text, APEX Calculus, which can also be downloaded from the website.

Printing the entire text as one volume makes for a large, heavy, cumbersome book. One can certainly only print the pages they currently need, but some prefer to have a nice, bound copy of the text. Therefore this text has been split into these three manageable parts, each of which can be purchased for about $15 at Amazon.com³.

Mathematics textbooks have a reputation for being hard to read. High—level mathematical writing often seeks to say much with few words, and this style often seeps into texts of lower—level topics. This book was written with the goal of being easier to read than many other calculus textbooks, without becoming too verbose.

Each chapter and section starts with an introduction of the coming material, hopefully setting the stage for “why you should care,” and ends with a look ahead to see how the just—learned material helps address future problems.

Versions 3.0 and 4.0 of the textbook include interactive, 3D graphics in the PDF version. Nearly all graphs of objects in space can be rotated, shifted, and zoomed in/out so the reader can better understand the object illustrated. However, the only pdf viewers that support these 3D graphics are Adobe Reader Acrobat (and only the versions for PC/Mac/Unix/Linux computers, not tablets or smartphones).

The latest version of the book, which is authored in PreTeXt, is available in HTML. In HTML, the 3D graphics are rendered using WebGL, and should work in any modern web browser.

Interactive graphics are no longer supported within the PDF, but clicking on any 3D graphic within the PDF will take you directly to the interactive version on the web.

APEX is a consortium of authors who collaborate to produce high quality, low cost textbooks. The current textbook—writing paradigm is facing a potential revolution as desktop publishing and electronic formats increase in popularity. However, writing a good textbook is no easy task, as the time requirements alone are substantial. It takes countless hours of work to produce text, write examples and exercises, edit and publish. Through collaboration, however, the cost to any individual can be lessened, allowing us to create texts that we freely distribute electronically and sell in printed form for an incredibly low cost. Having said that, nothing is entirely free; someone always bears some cost. This text “cost” the authors of this book their time, and that was not enough. APEX Calculus would not exist had not the Virginia Military Institute, through a generous Jackson—Hope grant, given the lead author significant time away from teaching so he could focus on this text.

Each text is available as a free .pdf, protected by a Creative Commons Attribution - Noncommercial 4.0 copyright. That means you can give the .pdf to anyone you like, print it in any form you like, and even edit the original content and redistribute it. If you do the latter, you must clearly reference this work and you cannot sell your edited work for money.

We encourage others to adapt this work to fit their own needs. One might add sections that are “missing” or remove sections that your students won’t need. The source files can be found at github.com/APEXCalculus⁴.

You can learn more at www.vmi.edu/APEX⁵.