a single new concept for the student to confront. This approach, which allows one to defer the notion of limits, can be justified using non-standard analysis. The results can, of course, be duplicated using limits - often with much more work.

The approach illustrated in this article differs in another significant way from that found in existing calculus textbooks. Almost all such textbooks seem to assume that a student learns the subject in a logically linear fashion. First we learn about functions and continuity, then about limits, then the derivative, and so forth. The student isn’t told, until somewhere around chapter 4 of the typical text, that all of this mathematical apparatus is somehow related to solving problems concerning motion, velocity, acceleration, and related concepts.

The present approach is structured to take into account that the learning of mathematics is a highly non-linear process. Oftentimes the mathematical (or “logical”) justification for a procedure cannot be understood by a student until long after the student has learned the procedure. All of us, I think, gain new insights into most topics in mathematics each time we revisit the topic. There is need, therefore, for texts that emphasize such revisitations as a part 