Crowell B. Brief Calculus 2005

Textbook in PDF format

This short introductory text focuses mainly on integration and differentiation of functions of a single variable, although iterated integrals are discussed. Infinitesimals are used when appropriate, and are treated more rigorously than in old books like Thompson's Calculus Made Easy, but in less detail than in Keisler's Elementary Calculus: An Approach Using Infinitesimals.
Numerical examples are given using the open-source computer algebra system Yacas, and Yacas is also used sometimes to cut down on the drudgery of symbolic techniques such as partial fractions. Proofs are given for all important results, but are often relegated to the back of the book, and the emphasis is on teaching the techniques of calculus rather than on abstract results.
Rates of Change
To infinity — and beyond!
Limits and continuity
Integration
Techniques
Improper integrals
Sequences and Series
Complex number techniques
Iterated integrals
Appendices
Detours
Answers and solutions
Photo Credits
References and Further Reading