Corrections

Chapter 2

Page 25:
equation (2.38)_2, last term should read ...g)T*k;
in (2.41), last term should be Ra Tk.

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.

Chapter 3

Page 42:
equation (3.39): minus sign missing, should be ...z^{-1}w^4 - z^{-1}(\frac{4}{9})w^6...

Chapter 4

Page 53:
line 6, irrotational -> incompressible

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.

Chapter 6

Page 94:
The displayed formula in the middle of the page, should have p_l-p_g=...+a\ddot{a}]-...

Chapter 10

Page 150:
Two lines above (10.20), and page 152, line above (10.26): the transformation should be t = p\tau/2f.

Chapter 12

Page 191:
Oops; air density is wrong below eq 12.56; correct values: c_0 = 0.4 x 10^-5, \rho = 0.5 x 10^-3 , which gives T_c = 924 K, rest is ok, though having \beta \sim \mu seems most natural.

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.

Chapter 18

Page 334:
(18.27) is correct, but the first exponent in (18.28) should be n, not n-1. There is a knock on effect in (18.29) (n -> n+1, and (18.30) and (18.31), where n+1 -> n+2. However, (18.32) is correct again.