Lecture 5, Friday, 9/5/08: Section 11.1: Vector-valued functions

Topics

Vector-valued functions: Definition and geometric interpretation as motion in space
Examples of vector valued functions: Line, helix
Arclength formula ((1.4), p. 859)

Read

Skim through Section 11.1. This is largely a picture section (the exception being the arclength formula, which you definitely have to know), so the "reading" is on the light side. However, you should at least take a look at the various curve plots given, and the corresponding equations, to get a feel of what these things look like. While I won't put graphing or curve-matching problems on tests, knowing what a given curve (roughly) looks like is a very useful skill that may come in handy in later sections. (You can skip over Examples 1.7 and 1.8.)

Homework

Section 11.1: 49 (This is the only exercise in this section on the arclength formula; Example 1.6 provides another illustration, involving a slightly trickier, but still doable, integral.)

Notes

Section 10.6 (Surfaces in Space) is independent from the rest of Chapter 10 and 11 and will be deferred till later.
For arclength integrals (and other integrals that will come up in later sections), you will need to know the basic integration techniques (e.g., substitution, and integration by parts).

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Last modified Mon 08 Sep 2008 09:41:26 AM CDT