Elementary Calculus: An Approach Using Infinitesimals
by H. Jerome Keisler
Publisher: Bodgen & Quigley 2012
Number of pages: 992
This is a calculus textbook at the college Freshman level based on Abraham Robinson's infinitesimals, which date from 1960. Robinson's modern infinitesimal approach puts the intuitive ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners to understand than the more common approach via limits.
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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.
This wikibook aims to be a quality calculus textbook through which users may master the discipline. Standard topics such as limits, differentiation and integration are covered as well as sequences and series, multivariable and differential calculus.
by William V. Smith - Brigham Young University
Here is a free online calculus course. This is essentially an ordinary text, but you can read it online. There are lots of exercises and examples. The text is rigorous. We do calculus in both one and two variables at the same time.
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.