Twenty Key Ideas in Beginning Calculus, Paperback/Dan Umbarger

Twenty Key Ideas in Beginning Calculus is a color 174 page book written by a high school mathematics teacher who learned how to sequence and present ideas over a 30-year career of teaching grade school mathematics. It is intended to serve as a bridge for beginning calculus students to study independently in preparation for a traditional calculus curriculum or as supplemental material for students who are currently in a calculus class. It is highly visual with 40 supportive images, 100+ cartoons and other illustrations, 110 graphs, and 40+ data tables spread throughout its 174 pages. Comprehension and understanding of ideas is emphasized over symbol manipulation although the latter is covered. The main text, Chapters 1-14, teaches "intuitive calculus," while the appendices contain "traditional calculus" proofs allowing the reader to customize their learning experience according to their ability and interest for rigor. When appropriate, the reader is referred to correlative interactive applets that can be used to supplement the text.