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William Freed

In Memoriam

William Freed
Associate Professor, Mathematics & Physics
Department of Mathematics

Teaching History

1962-1965 Goshen College – Goshen, Indiana
1965-1967 Middle East Technical University – Ankara, Turkey
1972-present, Concordia University of Edmonton – Edmonton, Alberta

Apex Infinitesimal Calculus Textbooks

Available for download below

Epsilon-delta calculus presents serious impediments to student learning and understanding of calculus for most students. Infinitesimal calculus requires only an algebra background possessed by most students.

All the theorems and formulas of calculus have intuitive derivations or proofs including more advanced ones such as the Extreme Value Theorem and the Riemann Integrability of Continuous Functions on a closed Interval.

Users of calculus typically misuse limit notation or ignore it completely. Did anyone ever invoke limits in the derivation of a physical or financial law or the Mean Value Theorem in an application of integration outside of a calculus course?

The textbooks are built on Gregory Hartman’s excellent, Creative Commons, Apex Calculus textbooks. I started this textbook in 2018. I have been teaching calculus using infinitesimal methods off and on since about 1980. The textbook was done as a pdf since it was the easiest way of combining my Mathematica notes and Hartman’s textbook. If there is sufficient interest, a LaTex version could follow. Long term hopes are to produce a version entirely devoid of limit methods.

Since this book is under Creative Commons production, you are free to use or adapt it for almost any non-profit use. I am interested in hearing your comments or results of its classroom use. I welcome suggestions for improvement or any level of collaboration.

Bill Freed


Click for downloads:

Apex Infinitesimal Calculus, Volume 1

Apex Infinitesimal Calculus, Volume 2