Winter 2003

This document details what ideas and topics will be taught in Math 116. The list of sections is almost an accurate description of what students need to know, but two sections are only partially taught, and others have some material excluded or emphasized. Most sections are marked "All", which means that all the material in that section is testable material.

Section	Relevant Material
3.8	All Despite the chapter number, this is a new section, with some very new ideas!
5.1-5.4	All. This is review from 115, and will be take up about two class days. Since this chapter lays the foundation for integral calculus, students should pay careful attention to anything here they don't already understand!
6.1-6.2	All. This is also review from 115. It will take up about one class day.
6.4	All.
7.1	All.
7.2	All.
7.3	All.
7.5	All. We used to distribute calculator programs to help with this material. Now we use java applets on this website as a "homework aid." Students will not need the calculator programs, but will need to know how to do Riemann sums by hand.
7.7	All, but students don't need to memorize the formula or understand the physics fact behind it:
7.8	All.
8.1	All.
8.2	All.
8.3	All.
8.5	Present and future value of lump sum payments and payment streams, but not consumer and producer surplus, which we shall leave to the economists. This also excludes "supply and demand curves" at the bottom of p. 380.
8.6	All.
8.7	All.
9.1	All.
9.2	All, including the extremely useful but sometimes missed (because of page layout) Theorem 9.3.
9.3	Only the "Comparison test for Series," which includes page 417 and half of page 418. The rest of this section (Positive and negative, ratio test, and alternating series) we will ignore. The partial section may take significantly less than one class day.
10.1	All. (We include the expansion about a point "a" other than zero.)
10.2	Almost all. But the section "Intervals of Convergence of Taylor Series" seems to depend on section 9.4, which we skip. Students should understand about Taylor series: That they generally converge on an interval. What convergence means numerically (for a fixed x, as n varies.) What convergence means graphically (how the graphs of the taylor polynomials relate to the graph of f(x) inside and outside the interval of convergence). That the interval of convergence is often the whole real line, and that this is the behavior of sin(x), cos(x), and ex. Students do not need to know: That there is a notion "Power Series" which is a natural generalization of Taylor Series. That the interval of convergence is a "ball" centered at the point of expansion. That there is therefore a "radius of convergence." How to calculate the radius of convergence.
10.3	All.
11.1	All.
11.2	All.
11.3	All.
11.4	All.
11.5	All.
11.6	All.
11.7	All.
11.8	All.