ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book provides a mathematical overview of differential and infinitesimal calculus. It looks at the place of limits and continuity in elementary calculus curricula and one well know curriculum, Advanced Placement Calculus, in particular. discusses prior knowledge and curricula matters, ways that differentiation can be introduced, the rules for differentiation, special functions, what derivatives tell the reader about functions and their graphs, tasks and an overview of education research on differentiation. The book presents the main ideas of integral calculus and the fundamental theorem of calculus (FTC). It considers aspects of calculus and/or real analysis courses that come after an elementary course in calculus. It could be argued that, apart from giving them practical arithmetic skills, one of the primary purposes of the secondary mathematics curriculum is to prepare students for the study of calculus.
