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where a1, a2, and a3 are real-number coefficients Let s go into Cartesian xyz space and restrict ourselves to a single plane in which the value of x is some real-number constant c This plane is parallel to the yz plane, and it intersects the x axis at the point (c,0,0) Consider a parabola in the plane x = c whose axis is parallel to the y axis, as shown in Fig 18-3 (The axis of a parabola is a straight line in the same plane as the parabola, and on either side of which the parabola is symmetrical) In this situation, the value of z tracks right along with the value of t, while the variable y follows f (t) Therefore x=c y = f (t) = a1t2 + a2t + a3 z=t The above set of equations is a parametric description of our parabola If we want to describe a parabola in the plane x = c whose axis is parallel the z axis instead of the y axis, then y follows t while z follows f (t), and we have x=c y=t z = f (t) = a1t2 + a2t + a3

Hold y constant Now suppose that we restrict our movements to a plane in which the value of y is always equal to a constant c The equation of the plane is y = c It s parallel to the xz plane, and it intersects the y axis at (0,c,0) Imagine a parabola in this plane whose axis is parallel to the z axis, as shown in Fig 18-4 In this situation, x follows t while z follows f (t), and the curve can be described as

As mentioned earlier, if a worker prepares his or her schedule early, and comes back to it later, it increases focus, motivation, and a sense of being respected as someone making a unique contribution to the project We increase project quality and reduce risk When the worker takes time to think things through, it is natural to come up with better ways of doing things and ways to prevent problems..

x=t y=c z = f (t) = a1t2 + a2t + a3 To describe a parabola in the plane y = c whose axis is parallel the x axis, we can let z follow t and let x follow f (t), getting the system x = f (t) = a1t2 + a2t + a3 y=c z=t

Hold z constant Finally, let s confine our attention to a single plane in which the value of z is some real-number constant c The plane z = c is parallel to the xy plane, and it intersects the z axis at (0,0,c)

You have written and organized the list How do you know you did not miss anything How do we verify that a WBS is complete and correct Here are the most important questions, from the bottom up Key Questions About Each Step: Verifying Each Step is Clear Each step of a project does something and delivers something Can you read each step and say what will be done, and what will be delivered Each step should contain a verb describing what will be done, and a noun describing what will be delivered For example, here are several badly written steps (and what is wrong with them): Security plan (no verb) Plan security (verb and noun both too vague) Design security plan (verb and noun do not match) If you see an item like any of the above, change it to: Write security plan Here, the step is clear.

(0, c, 0)

It is possible to create a cont.roller with a continuous nonlinear function whose gain increases with amplitude. In contrast to the three-state controller, its gain in the region of zero error would be greater than zero, with integrating action to avoid offset. But its change in gain with amplitude should be less severe than that of a dual-mode system. T h u s it would be more tolerant of inaccuracy in the control parameters. The continuous nonlinear controller could be mathematically described by the expression

Figure 18-4

Parabola in a plane where y is held to a constant value c The plane is perpendicular to the y axis, and intersects that axis at the point (0,c,0)