Is calculus really that different from algebra? A more logical way to understand and teach calculus

Abstract

To say that the teaching of calculus has not changed much since the time of Newton and Liebnitz may be overkill; however, as far as this researcher knows, neither at present nor at any time in the past, have there been textbooks that teach calculus as the logical extension of algebra. The intent of this paper is to discard the blinders that have hampered the traditional teaching of calculus and, conceptually, re‐examine some of the intuitive ideas that underlie this subject matter. In particular, this paper examines the various indeterminant forms that arise through the blind application of algebraic operations. Furthermore, to exactly two of these indeterminant forms there exists an interpretation that is one of the fundamental operations that comprise the subject matter normally referred to as ‘calculus’, and to a third there is associated a fundamental number that is the most important constant of calculus.