EJMT Abstract

We give an intuitive definition for derivative of a function at a point without using the epsilon and delta concept, which leads to the concept of integration and the outcome of the Fundamental Theorem of Calculus (FTC). We include the use of graphical representations to strengthen the understandings of our definitions on differentiation and integration. All of our constructions do not depend on axiom of completeness of real numbers. This paper is intended for two purposes: First is to makes the concepts of differentiation and integration more accessible to beginners who start learning Calculus; second is to give those who have learned Calculus and beyond to ponder if approaches described in this article can be adapted in teaching Calculus in their respective countries.