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d2y dy 2 + y = (t 1), y(0) = y '(0) = 0. dt dt 2 equation = y''[t] 2 y'[t] + y[t] DiracDelta[t 1]; LaplaceTransform[y[t],t,s]+ s2 LaplaceTransform[y[t],t,s]

prescriptive; that is, the software process model can describe what is supposed to happen. Prescriptive software process models can be used to describe the standard software development process. These can be used as training tools for new hires, for reference for uncommon occurrences, and for documenting what is supposed to be happening.

s 2(s LaplaceTransform[y[t],t,s] y[0]) s y[0] y'[0] s [

NOTE: The iPad may ask you to move away from any source of interference while you go through the calibration process. 6. Hold your iPad level to the ground. If you calibrated it successfully, the compass will rotate and point north.

temp = LaplaceTransform[equation, t, s]

temp2 = Solve[temp, LaplaceTransform[y[t], t, s]] /. {y'[0] 0, y[0] 0}

In this chapter, we will give you an overview of the Notes app, which you can use to write notes, make grocery lists, and make lists of movies you d like to watch or books you d like to read. We will show you how to organize and even email notes to yourself or others. Ideally, we hope that Notes will become so easy on the iPad that you can eventually get rid of most, if not all, of your paper sticky notes!

Figure 2-1 is a process model for unit testing software. There are two actors: the tester and the team leader. The unit tester, of course, is responsible for the unit testing. The unit tester uses the source code and the test plan to accomplish the unit testing. The result of this activity is an artifact, the test results. The team leader reviews the test results, and the result of this activity should be the approval of the unit testing. This model does not explicitly show what happens when the process is not successful. It could be inferred that the unit tester keeps testing until he or she is happy. Similarly, if the team leader is not ready to give the approval, then the process may be backed up to redo the unit testing.

LaplaceTransform[y[t],t,s]

temp3 = temp2[[1, 1, 2]] s 1 2 s + s2 solution[t_] = InverseLaplaceTransform[temp3, s, t] 1+t ( 1 + t)HeavisideTheta[ 1 + t]

In addition to the built-in Notes app, there are a number of free or low-cost note applications you can obtain from the App Store. We will show you how to use one of these note apps called Evernote later in this chapter. This app is quite powerful and allows you to sync notes wirelessly with a web site, store and organize voice notes, add pictures and other mixed media to your notes.

Plot[solution[t], {t, 0, 2}, PlotStyle Thickness[.01]]

2.5 2.0 1.5 1.0 0.5

Fig. 2-1.

TIP: The Notes app that comes with the iPad is pretty basic and utilitarian. If you need a more robust notes application that you can sort, categorize, import items into (PDF, Word, and so on), have folders, search, and more; you should check out the App Store on your iPad. Do a search for notes, and you will find at least a dozen notes-related apps ranging from $0.99 and up.

Laplace transforms can be used to solve systems of differential equations. The technique is similar to that of a single equation, except that a different transform is defined for each dependent variable. The next example illustrates the method for solving a system of two first-order equations. It generalizes in a natural way to larger and higher-order systems.