Inside Calculus

Preliminary Text. Do not use. This book presents the theoretical pieces of introductory calculus in a style suitable to accompany almost any first calculus text. It offers a large range of increasingly sophisticated examples and problems to build understanding of the notion of limit and other theoretical concepts. It is aimed at students who will study fields in which the understanding of calculus as a tool is not sufficient. The text uses the "spiral approach" of teaching, and may be used as the "content" text for a transition to upper level mathematics course.

Résumé
Aimed at students who will study fields in which the understanding of calculus as a tool is not sufficient, the text uses the "spiral approach" of teaching, returning again and again to difficult topics, anticipating such returns across the calculus courses in preparation for the first analysis course.

Contenu
Limits.- Continuity.- The Language of Theorems.- Theorems about Continuous functions.- Limit Proofs.- Limit Theorems.- Which Functions are Continuous?.- Derivatives.- Theorems about the Derivative.- Other Limits.