Chapter 2 starts out with a physics motivation, chosen to be the experimental study of the photoelectric effect by Millikan. It then discusses the concepts of absolute and relative error, as well as eror propagation in general. It then goes on to discuss the representation of real numbers on the computer, touching on topics like overflow, machine precision, and catastrophic cancellation. It then addresses a variety of problems where rounding error becomes significant: compensated summation, analytic manipulation, Taylor series, and recursion. The chapter is rounded out by a physics project, which studies the multipole expansion in electromagnetism, and a problem set. The physics project provides an opportunity to introduce Legendre polynomials, which play an important role in the following chapters.

The objective of this chapter is to discuss the error propagation through computation from the error contained in the original data. We are not focusing on the measurement errors themselves, although the propagation of computational error is related to measurement errors. We also discuss the variability propagation with given mathematical relationships, or sensitivity of a system to a given parameter, which are all closely related to error propagation.