Howland (mathematics, University of Virginia, emeritus) draws on his years of teaching for this textbook introducing students to single variable calculus. He warns that it is a subject one cannot skim and lays out each proof in clear steps. The subject is introduced in the first chapter: number systems, sequences, properties and infinite limits and continuity. Later chapters cover derivatives, integrals, infinite series, uniform convergence. this leads to a discussion of Taylor's Theorem, Abel's summation by parts and differences between Abel and Tuber's theorems. Each chapter concludes with a set of problems for the student to solve. Howland also provides appendices on typology and on set theory for professors who wish to include these in the course. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)