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First we graph the equations. ContourPlot[{Exp[x] + Log[y] 2, Sin[x] + Cos[y] 1}, {x, 0, 2}, {y, 0, 3}, Frame False, Axes True]

It appears that there is only one solution. We use x = 1, y = 1 for our initial guess. FindRoot[{Exp[x] + Log[y] 2, Sin[x] + Cos[y] 1}, {x, 1}, {y, 1}]

Almost every view from your iPod app (Playlists, Artists, Videos, Songs, etc.) has a search window in the upper right corner, as shown in Figure 7 2. Tap once in that search window and type a few letters of the name of an artist, playlist, video, or song to instantly see a list of all matching items. This is the best way to quickly find something to listen to or watch on your iPad.

0.624295, y 1.14233}

If the function in an equation is such that its evaluation is costly, particularly if high precision is desired, there is another procedure that may be beneficial.

See Fig. 11-12.

The iPod app is very flexible when it comes to ways of displaying and categorizing your music. Sometimes, you might want to look at your songs listed by the artist.. Other times, you might want to see a particular album or song. The iPad lets you easily change the view to help manage and play just the music you want at a given moment.

Whereas FindRoot uses linear functions (straight lines) to approximate the root of the equation, InterpolateRoot uses polynomials of degree 3 or less. The result is that higher precision can be achieved with fewer function evaluations. InterpolateRoot is contained within the package FunctionApproximations` and must be loaded prior to use. As with FindRoot, the equation may be replaced by a function, in which case its zero is computed.

This example computes the zero (between 2 and 3) of the Bessel function2 J0(x), using a working precision of 1000 significant digits. For comparison purposes, the Mathematica function Timing is used. The actual numerical approximation is suppressed to save space. As a result, the value Null is returned. Delete the semicolon and run the command to see the actual result of the calculation.

The Artists view lists all the artists on your iPad, or, if you are in a playlist and select Artists, it will list the artists in that playlist. Flick through the list to move to the first letter of the artist s name you are looking for. When you find the artist s name, touch that name and all the songs by that artist will be listed, with a picture of the album art to the left. TIP: Use the same navigation and search features as you do with your Contacts app (the address book).

{0.219,

B&B 1 1 1..n calendar 1 0..n 0..n reservation 1..n bedroom 1 0..n payment expense 1 0..n 1 0..n transaction

Null}

Touching the Songs tab shows you a list of every song on your iPad. If you know the exact name of the song, flick through the list or touch the first letter of the song in the alphabetical list to the right.

FunctionApproximations` InterpolateRoot[BesselJ[0, x], {x, 2, 3}, WorkingPrecision 1000]; //Timing

{0.046,

The music on your iPad is also organized by albums, which you ll see when you touch the Albums tab at the bottom. Again, you can scroll through the album covers or touch the first letter of the album name in the alphabetical list and then make your selection. Once you choose an album, all the songs on that album will be listed. To close the pop-up window with the list of songs, simply tap anywhere outside that window.

Fig. 11-12.

Null}

Since 5 cos x = 4 x 3 if and only if 5 cos x 4 + x 3 = 0 , we introduce the function f ( x ) = 5 cos x 4 + x 3 and look for x-intercepts. (Although we could look for the intersection of two curves, it is easier to approximate where points intercept an axis.) f[x_] = 5 Cos [x] 4 + x3; Plot[f[x], {x, 1, 2}]