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This text comprises a three–volume series on Calculus. The first part covers material taught in many “Calculus 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6. The second text covers material often taught in “Calculus 2”: integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 7 through 10. The third text covers topics common in “Calculus 3” or “Multivariable Calculus”: parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 11 through 15. All three are available separately for free.

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 downloaded separately.

The source files for the text can be found at

This edition has been superseded. The 2nd edition is available here:



Publication Date


Document Type



Grand Forks, ND


Calculus; Textbooks

Personal Subjects

Corral, Michael; Dawkins, Paul Christian; Heinold, Brian; Siemers, Troy; Chalishajar, Dimplekumar; Bowen, Jennifer(Jennifer Lynne)




Starting with the source at, faculty at the University of North Dakota made several substantial changes to create APEX Late Transcendentals. The most obvious change was to rearrange the text to delay proving the derivative of transcendental functions until Calculus 2. UND added Sections 7.1 and 7.3, adapted several sections from other resources, created the prerequisite sections, included links to videos and Geogebra, and added several examples and exercises. In the end, every section had some changes (some more substantial than others), resulting in a document that is about 20% longer. The source files can now be found at

Extra thanks are due to Michael Corral for allowing us to use portions of his Vector Calculus, available at (specifically, Sections 11.7, 13.9, and 14.7, and Chapter 15) and to Paul Dawkins for allowing us to use portions of his online math notes from (specifically, Sections 8.5 and 9.7, as well as “Area with Parametric Equations” in Section 10.3). The work on Calculus III was partially supported by the NDUS OER Initiative.

Updated: July 27, 2017

Creative Commons License

Creative Commons Attribution-NonCommercial 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License

APEX Calculus: UND Edition

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