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If you have already worked out the milestones for phases in the project overview, that is all you need. If you have not, you can write down just three or four things you know you need to do. They do not have to be in the right order. You do not have to know how you would do them. We are just getting a seed, and we will grow the list from that. For example, suppose you are building a small web page for your own company. It will be a simple brochure with no shopping cart and no fancy database. Your rst list might look like this: Learn Microsoft FrontPage 2002. Get graphics. Find an internet service provider (ISP) to host the site. Get text from marketing and public a airs.

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Figure 17-11

Figure 17-11 shows a perspective on Cartesian xyz space that we haven t seen before We re looking down on the yz plane from somewhere near the positive x axis Nevertheless, the axes are correctly oriented with respect to each other, as you can verify by referring back to Chap 7 Let s stay with this axis orientation as we look at the next couple of objects

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Next, you want to make sure you have got all the steps. There are two things you should do: picture the steps and ask an expert. Picture the Steps First, picture doing the rst step on the list. Imagine it clearly, ngers on the keyboard, launching FrontPage 2002. Have someone ask you: Could you do this step right now, or is there something else you need to do rst Then you realize, Learn it I don t even own it. Besides, I always learn software from books. So I d better buy some books.

Hyperboloid of two sheets Figure 17-12 shows a hyperboloid of two sheets, which is the graph in Cartesian xyz space of an equation having the form

x2/a2 + y2/b2 z2/c2 = 1 where a, b, and c are positive real-number constants Here, we have two surfaces that resemble bowls facing in opposite directions In theory, the bowls extend infinitely toward the left and the right in this illustration Both surfaces share a common straight-line axis that coincides with the coordinate y axis, and the two sheets are exact mirror images of each other The center of the entire hyperboloid is at the origin The contours of the surfaces depend on the values of a, b, and c

Figure 17-12

From this, you add two tasks to your list: Buy FrontPage 2002. Buy books about FrontPage 2002.

If we make the term containing x2 positive instead of the term containing y2, we get the general equation x2/a2 y2/b2 z2/c2 = 1 which produces a hyperboloid of two sheets whose axis lies along the coordinate x axis, and whose center is at the origin If we move the plus sign so it s in front of the term containing z2, the general equation becomes x2/a2 y2/b2 + z2/c2 = 1 This maneuver gives us a hyperboloid of two sheets whose axis lies along the coordinate z axis, and whose center is at the origin

With the existing settings, the control loop limit-cycles at an amplitude of 1.8H and a period of 24.4~~. Reduction of the proportional band by half will change the amplitude only to 2H but will reduce the period to 127d. Minimum period may be attained by reducing the proportional band to the point, where the amplitude becomes objectionable. Increasing

Elliptic cone Figure 17-13 shows an elliptic cone It s what we get when we graph an equation of the form

Picturing the steps leads to results that seem obvious, even too simple to believe. But they are obvious only to you, in your situation. Another person, or a person in a di erent situation, would have a completely di erent list of obvious steps. Someone else might say, Learn it, are you kidding I haven t had time to learn new software in ten years! And we don t even own it. Maybe we won t need to buy it. For this person, the list becomes: Hire a consultant who builds web pages in FrontPage 2002. Ask the consultant if we are going to have to own our own copy. If we will, order it and decide which member of the team is going to learn to use it.

x2/a2 + y2/b2 z2/c2 = 0 where a, b, and c are positive real-number constants The perpendicular cross sections of the cone are always circles or ellipses The cone s axis coincides with the coordinate z axis, and the cone s vertex coincides with the origin The flare angles, as well as the eccentricity of the crosssectional ellipses, depend on the values of a, b, and c

Figure 17-13