Page 31:
Exercise 2.3. This is just used as an exercise in scaling, but there
are a couple of omissions, which become more important if the sub-text
is considered. Just above the diagram on page 31, v/v_0 should
obviously be |v|/v_0. On line 2 of page 32, x
should be x_j, and in part (iv) line 3, there should be
"...approximately, if u_t > 0, by".
The point is, that the fast time behaviour represents earthquakes, in which (we expect) u_t > 0, while in the slow phase, there is no motion. So the reason to have u_t > 0 in the fast phase is that this is appropriate in earthquakes. However, it is not appropriate for analysing linear stability, and strictly the last part requires the friction law with the modulus sign.
In fact, sgn(w) should be interpreted here as -1 < sgn(w) < 1 if w = 0, to allow for static friction. It is then easy to analyse the relaxational motion in the phase plane, in the absence of spatial variation.
See also the chapter 2 notes.
Question 5, the displayed formula should have ...- \frac{1}{4} ... (minus not plus). Thanks to Tom Witelski of Duke University and his students for this.
Page 199:
Eq. (12.110) The square bracket term in the denominator should be
squared: [1+|w|^2]^2.
Eq. (12.112) q definition should be 2+r\theta'.
Page 200:
Exercise 5. \beta >> \delta in line 4.
Exercise 6. Line 5: \theta\sim\beta/\mu and also \theta = \beta\Theta/\mu.