An Example Outline

I have mentioned the idea of creating an outline a few times during class. It might be a good idea to present an example, so that we can have something concrete to deal with. Since we covered sections 3.1 and 3.2 in class today, I will give my outline for section 3.1.

I usually try to keep my outline down to three or four key points for each section. For this particular section, I found these points to be the most important:

1. Extrema
2. Critical Point
3. Locating extrema on an interval

This is the start of my outline. There are several criteria to think about when deciding what you will want in your outline. Are there any new words? That is, are the authors using terminology that you haven't seen before? If so, they are probably trying to tell you about a new idea. You should make a note of that, as it might be something you want in your outline. Notice, the authors have not used the words "extrema" or "critical point" before in previous sections. That's why they found their way onto my list. Another idea to keep in mind are procedures and concepts that get used for multiple problems in the exercise set. That indicates that the authors (and the instructor) want you to get practice with these. Probably because they'll show up on a test.

Notice that a the start of the last paragraph, I was careful to say that "This is the start...". If this outline is going to be useful to me later on, such as when I'm studying for a test, I'll need to include more than just the terms themselves. Write down what they mean and give a simple example of each. Looking at my list, I started out with something like this.

You'll notice that my definition does not precisely match the definition that our textbook gives. That's OK. These outlines don't have to be perfect. They should give us an effective way of thinking about the idea, contain enough information so that we can refer to it after few weeks have passed and still be able to understand the ideas.

Continuing with my outline, I might draw pictures that remind me of the different types of critical points a function can have. Lastly, I would write down the procedure for finding the extrema of a function on an interval, writing down an example problem from the notes or from the exercises so that I could go back later an see how each step works.

I would keep my outline separate from the rest of my notes. Further, I would add to this outline as we go through the succesive sections and chapters of the text. Going through the outline each day before you work on your exercises should prove to be quite valuable. It will help fix the important topics in your mind, and let you know where you should concentrate when you are studying for the exams. When you get to the end of the course your outline can serve as a review for the final exam.