An elementary, limit-free calculus for polynomials

Abstract

This work grew out of a simple problem: how could I introduce the basic concepts of calculus to students who were mathematically under-prepared? It has been pointed out by many authors (see [1] and its references) that limits are a major stumbling block for many students beginning their study of calculus. Part of the difficulty with limits is the conceptual confusion between process and value . Some limits can be evaluated by a simple process of substitution, for example, while others cannot, for example,