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TODO
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TODO
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* Make everything be in some subsection, the "introduction" divisions in
pretext may be screwing up and just dropping certain things on the floor.
This requires a new edition since there are going to be probably page
number changes. If this is done, we could drop the manual introduction
%mbxINTROSUBSECTION thing and do it automatically again perhaps.
Pretext/HTML:
* https://pretextbook.org/doc/guide/html/processing-directory-management.html
Further down the road perhaps (some of them could be doable in next
minor version):
SMALLER THINGS MAYBE:
* Add smallish subsection to 6.2 about transform of periodic functions.
After that, readd the WeBWorK exercises with the periodic functions.
* Expand discussion of vector fields and how they are drawn in 3.1.
* Add maybe a few more exercises for setting up applications in 3.1
* In 3.6 add more exercises on forced, and also improve the exposition wrt
the units.
* In 3.4 (or earlier?) Add some exercises on constant nonhomogeneity for
an invertible A, that just translates the point.
* Include annihilator method at least in exercises of section of 2.5
* Perhaps change name of \vec{x}_1 solutions to avoid confusion with x_1
components, see what other books do.
* Add factorization idea in wave equation (d'Alembert) to write it as
two vector fields applied to y perhaps? Makes more sense if we have
first order before this.
* Perhaps mention somewhere in 2.2 how the correspondence is with $y^{(n)}$
going to $r^n$ in the characteristic equation, might make it simpler to
see.
* More detail in 7.1, work more with the expanded series
* Another example in 7.2, perhaps nonlinear to show that one can keep
cranking out the coefficients.
LARGER THINGS MAYBE:
MAYBE IN CASE OF BIG CHANGE (incompatible edition) in the Star Trek
future (quite probably never):
* Split Fourier Series - PDE, probably move the "applications of eigen-series"
to the PDE chapter. In this case, first order PDEs might make sense
before the second order ones since it leads naturally into d'Alembert,
but they are in chapter 1, where they might make more sense.
This requires much more thought, maybe forget about it.
PROBABLY NOT/VAGUE:
* Perhaps an appendix with more info on existence uniqueness, linear
independence (maybe wronskian, though perhaps it might be best to avoid
wronskian, to avoid plug and play maddness), some proofs and extra
information in general, basically some extra optional sections. etc..
Need more ideas for this.