Appendix D

Formula Derivation in Chapter 7

The derivation of Eq. (7.11) is as follows:

(D.1)

Thus,

(D.2)

Using Eqs. (7.5) and (7.8), the gradient above can be written as

(D.3)

The derivation of Eq. (7.20) is as follows:

(D.4)

Thus,

(D.5)

Using Eqs. (7.8) and (7.18), the gradient above can be written as

(D.6)