Precalculus.pdf

Precalculus

David H. Collingwood

Department of Mathematics

University of Washington

K. David Prince

Minority Science and Engineering Program

College of Engineering

University of Washington

August 30, 2007

2003 David H. Collingwood and K. David Prince. Permission is

granted to copy, distribute and/or modify this document under the terms of the

GNU Free Documentation License, Version 1.1 or any later version published by

the Free Software Foundation; with no Invariant Sections, with no Front-Cover,

and with no Back-Cover Texts. A copy of the license is included in the section

entitled GNU Free Documentation License.

Author Note

For most of you, this course will be unlike any mathematics course you

have previously encountered. Why is this?

Learning a new language

Colleges and universities have been designed to help us discover, share

and apply knowledge. As a student, the preparation required to carry out

this three part mission varies widely, depending upon the chosen eld of

study. One fundamental prerequisite is uency in a basic language;

this provides a common framework in which to exchange ideas, care-

fully formulate problems and actively work toward their solutions. In

modern science and engineering, college mathematics has become this

basic language, beginning with precalculus, moving into calculus and

progressing into more advanced courses. The difculty is that college

mathematics will involve genuinely new ideas and the mystery of this

unknown can be sort of intimidating. However, everyone in this course

has the intelligence to succeed!

Is this course the same as high school Precalculus?

There are key differences between the way teaching and learning takes

place in high schools and universities. Our goal is much more than just

getting you to reproduce what was done in the classroom. Here are some

key points to keep in mind:

The pace of this course will be faster than a high school class in

precalculus. Above that, we aim for greater command of the ma-

terial, especially the ability to extend what we have learned to new

situations.

This course aims to help you build the stamina required to solve

challenging and lengthy multi-step problems.

As a rule of thumb, this course should on average take 15 hours

of effort per week. That means that in addition to the 5 classroom

hours per week, you would spend 10 hours extra on the class. This

is only an average and my experience has shown that 1215 hours

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