Math 520, spring, 1998.
Analysis is the branch of mathematics that grew out of trying to understand why calculus works.
But the roots of analysis came long before calculus, with attempts to calculate areas using infinitary processes. The book we are using takes a historical approach. Then we will move on to some of the specific concerns that gave rise to calculus. Only in chapter 6 will we begin the logically rigorous justification of calculus. This justification didn t develop until the early 19th century and wasn t completed until the late 19th century.