Many problems give rise to integrals you cannot do. We will look at how to use numerical methods to give an estimate to within a known error. Note that without a bound on the error an estimate is useless, since all you know about it is that it is a number which isn't exactly the one you want. Indeterminant forms and improper integrals provide a useful tool in the study of series and a way to explore the relative rates of growth of polynomials, exponentials, and logarithms. After spring break we will shift our focus to the study of infinite series.
Several test are available to determine when series converge.
Tying the series to the process of function approximation helps us see which tests to use first. Alternating series give particularly useful approximations because they have easily obtained error estimates. See the calendar for tentative dates. I will assign homework daily, to be handed in on Monday. Some will be routine exercises you need to practice on to develop technique, some will be projects aimed at deeper understanding or more realistic applications.