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During the first week of the semester it is difficult to get started with the
course material. Some students have not settled in, some are still changing
sections, and some still have to sign up for a course. For this reason, it is
reasonable to teach an interesting, relevant topic that is somewhat independent of the course. Some instructors in a calculus course use the first week
to review topics from precalculus. Instead, we decided to spend this week
on vectors and the geometry of the plane, topics that other sciences and
engineering like to see covered early. These notes are meant as lecture notes
for a one-week introduction.
There is nothing original in these notes. The material can be found
in many places. Many calculus books will have a section on vectors in the
second half, but students would not like to start reading there. The material
is also contained in a variety of other mathematics books, but then we would
not want to force students to acquire another book. For these reasons, we
are providing these notes.
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