Slice selection in MRI Looking at some examples in the "handbook of MRI Pulse Sequences" by Bernstein, I see the following:

So if I can generate an RF pulse with a bandwidth of 2 kHz and I want a 3 mm slice thickness, the gradient amplitude can be chosen with:

$$
G_z = \frac{2\pi \Delta f}{\gamma \Delta_z}
$$

Plugging the values, this gives a gradient strength of 15.6 mT/m. 

Now, my question is that will this gradient select a 3 mm thick slice at the magnet isocenter?

Now say in my MR experiment I am acquiring 128 such slices. Now, if I want to excite the "bottom most slice" than I need to adjust the RF bandwidth and the change in RF BW is given by:

$$
\delta f = \frac{\gamma G_z \delta_z}{2 \pi}
$$

Here now, my $\delta_z = -64 * 0.003 m$. Hence, the new RF BW will need to be 

$$
f = \Delta f - 64 \Delta f = -126 khz
$$

I am not sure if this calculation is correct. The RF value seems quite high to be although I am not sure what is the range of modern MR scanner RF generators.
The bandwidth of the RF pulse does not change at all - it is the center-frequency of the RF-pulse that needs to be adjusted. The slice thickness is related to the frequency spread caused by your slice-selection gradient (as you see in the first formula). Hence, to achieve the same slice thickness for each slice, the RF bandwith may not change, but the RF center frequency.