Foundations of Infinitesimal Calculus
by H. Jerome Keisler
Publisher: University of Wisconsin 2011
Number of pages: 213
This monograph is a companion to the online edition of my textbook 'Elementary Calculus: An Approach Using Infinitesimals'. It can be used as a quick introduction to the infinitesimal approach to calculus for mathematicians, as background material for instructors, or as a text for an undergraduate seminar.
Home page url
Download or read it online for free here:
by H. Jerome Keisler - Bodgen & Quigley
This is a calculus textbook at the college Freshman level based on infinitesimals. This approach puts the ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners than the more common approach via limits.
by Robert H. Smith - Griffin
This work presents the leading features in the study and application of the higher mathematics. The development of the subject is based on essentially concrete conceptions, and no appeal is made to what may be termed rational imagination.
by Kenneth Kuttler
Calculus and many of its applications are discussed in this book. The reader should have a good understanding of algebra as well as geometry and trigonometry. There is also lots of non standard material, like some theorems of advanced calculus.
by Viktor Blasjo - Intellectual Mathematics
A concise textbook covering precalculus through vector calculus and differential equations using informal infinitesimal reasoning. Always gives the most illuminating proofs possible, while standard books obscure key ideas under pedantic formalism.