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 W.P. Webber, L.C. Plant - John Wiley & sons
The present text is the result of several years of study and trial in the classroom in an effort to make an introduction to college mathematics more effective and better suited to its place in a scheme of education under modern conditions of life.
by J. Nicholas, J. Hunter, J. Hargreaves - University of Sydney
Table of contents: Functions (Definition of a function, Domain and range of a function, Specifying or restricting the domain of a function); More about functions; Piecewise functions and solving inequalities; Polynomials; Solutions to exercises.
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 Jerrold E. Marsden, Alan Weinstein - Springer
The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. The exercise sets have been carefully constructed to be of maximum use to the students.