page 3: proposed change is ok

page 8: "higher-order derivatives" is ok

page 8: added "in" is *not* ok. One could just write
"... uncurled induction equation takes the form".
Alternatively, one could write:
"... uncurled induction equation, Equation 2, takes the form".
but this is more clumsy.

page 8: "subscript added to z" is *not* ok.
In both lines, it should just read "kz", i.e., k multiplied by z.
No extra space is needed here.

page 8: I suggest to write:
 "One of the higher-order derivative contributions to ..."

page 8: regarding the section number, change text to:
"will be discussed in section 4.1: ..."

page 17: writing ", such as" is ok.

I also noticed this: page 40, last line, in Reference
Elstner D, ..., change Rudiger -> R\"udiger