Bringing Rigor into Calculus
Bob Brabenec
Department of Mathematics
Wheaton College
For most calculus students, calculus is not much more than an amazing collection of formulas and techniques involving derivatives and integrals. What makes calculus so useful is the fundamental relationship between these two concepts that was discovered by Newton in the 1660s. For the next 150 years, calculus was successfully applied to solve a wide range of problems from the physical world. But this amazing structure of results had no solid foundation, and paradoxes began to appear. During the years from 1820 to 1870, most of these problems were resolved, and calculus was put into its modern form with all the concepts based on the limit definition. This gradual process of bringing rigor into the calculus led to the subject we usually refer to as real analysis. The historical development of calculus and analysis is also covered in this talk.