A Sensible approach to the Calculus

Abstract

In recent years, reform calculus has used the computer to show dynamic visual graphics and to offer previously unimaginable power of numeric and symbolic computation. Yet the available technology has far greater potential to allow students (and mathematicians) to make sense of the ideas. A sensible approach to the calculus builds on the evidence of our human senses and uses these insights as a meaningful basis for various later developments, from practical calculus for applications to theoretical developments in mathematical analysis and even to a logical approach in using infinitesimals. Its major advantage is that it need not be based initially on concepts known to cause student difficulty, but allows fundamental ideas of the calculus to develop naturally from sensible origins.