Calculus Deconstructed: A Second Course in First-Year Calculus, Calculus Deconstructed: A Second Course in First-Year Calculus

A thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous exposure to calculus techniques but not to methods of proof, this book is appropriate for a beginning Honors Calculus course assuming high school calculus or a “bridge course” using basic analysis to motivate and illustrate mathematical rigor. It can serve as a combination textbook and reference book for individual self-study. Standard topics and techniques in single-variable calculus are presented in the context of a coherent logical structure, building on familiar properties of real numbers and teaching methods of proof by example along the way. Numerous examples reinforce both practical and theoretical understanding, and extensive historical notes explore the arguments of the originators of the subject.No previous experience with mathematical proof is assumed: rhetorical strategies and techniques of proof (reductio ad absurdum, induction, contrapositives, etc.) are introduced by example along the way. Between the text and the exercises, proofs are available for all the basic results of calculus for functions of one real variable.