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Subject: Transfer function reduction math
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The "Lecture Notes in Control and Information Sciences" can be a 
fascinating book to page through, particularly if you can get your hands 
on a hard copy.

The particular one I'm looking through is from the early 1980s and 
there's a lot of interesting material related to optimization problems 
here, like "Optimal turning strategy for a supercruiser" (aircraft) and 
"Optimal maintenance policy and sale date for a machine with random 
deterioration and subject to random catastrophic failure"...

A fair bit of the mathematics assumes a certain baseline knowledge of 
the field of systems optimization/linear programming/etc and I don't 
easily follow most papers, but there are some papers of interest to 
electrical engineering, e.g. one about reduction of order of transfer 
functions using a minimum-phase approximation, higher order transfer 
functions sometimes contain more information than you need for a 
restricted bandwidth.

Unfortunately partly due to the pre-Latex typesetting e I'm unclear what 
this one is saying exactly:

<https://imgur.com/a/9HIKOEN>

  H(s) is just a regular s-domain transfer function with polynomials top 
and bottom, so they decompose it into odd and even parts and set it 
equal to...what's tanh phi(s) supposed to mean? Tanh(s)phi(s)? 
Tanh(phi(s))?

Seems like they're doing some kind of tanh interpolation but it's not 
entirely obvious to me how they get from equation (3) to the expression 
in (5).