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Math 15 Course Text Philosophy:

The material that comprises Math 15 is some of the most interesting in all of calculus. There is a wide range of topics addressed, and most of them can be approached more than one way. Indeed, it is the many levels of connections within the subject that makes it so interesting.

The textbook we are using (and, indeed, most traditional calculus texts) tends to treat all the topics as separate, unrelated ones. It also tends to gloss over some crucial issues dealing with the distinctions between graphs, images and implicit functions. Students traditionally find this a source of confusion, so we will try to make the differences more clear. Whenever we develop a new idea, we will see how it can be represented in each of the three forms. We also will give methods for converting from one to another, when this is possible. The book switches around between them without letting you know, but we will try to be more explicit about it.

The book also does not treat the topic of parametric representations very well, particularly in terms of surfaces in space. These will come naturally from our treatments of functions in general, and will play an important role in our course. They are one of the most useful forms for doing computer-based graphics, and so deserve a more careful treatment than they are given in traditional calculus texts.

Finally, we will spend about two weeks doing some topics in linear algebra, and this material is covered in a supplement to the book. This will be handed out when we begin that section of the course.

As a result of these issues, we will not be following the book closely. We will jump around between sections of the book, and even within a section, so please try to be aware of were we are. The course outline lists the appropriate sections for each topic. Note that not all topics have corresponding sections, as the books does not treat these topics. My organization of the material is quite different from the books; that doesn't mean mine is wrong, nor does it mean that the book's is wrong. They are just different. There are many ways to organize the material in this course, and I tend to do it differently each time I teach it. Each organization has its advantages and disadvantages. I hope you will bear with me in departing from the one used by the book; the payoff will be that your understanding of the topic should be better in the end.

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Comments to: dpvc@union.edu
Created: Jan 13 1998 --- Last modified: Jan 13, 1998 2:01:10 PM