The statement of a theorem has two parts
-- the premises, and
-- the conclusions.
1) You can't conclude the conclusions if you haven't established the
premises. For example, the conclusion of the Pythagorean theorem is
a^b + b^2 = c^2
but that only applies given certain premises, such as
-- a, b, and c are the lengths of the sides of a triangle
-- it is a right triangle, with c being the hypotenuse
-- Euclidean (as opposed to spherical) geometry.
2) There is no continuity in the space of theorems. If "most" of the
premises hold, it does not follow that "most" of the conclusions hold.
Starting at the bottom page 1 it says:
"Represent the object as a small box moving along a curved
path, rather than as an abstract dot."
A paragraph or so later it states the "Work / Kinetic Energy" theorem and
says we should
"Derive this from N2 and kinematics."
and goes on to apply the theorem to situations such as books sliding on
tables under the influence of friction.
The problem is that you cannot derive any such theorem that can be applied
in this way. The theorem as usually derived applies only to point
particles ("dots") or objects with no internal degrees of freedom.
You simply cannot apply the F dot ds formula to the total macroscopic force
(F) on the book and its average macroscopic motion (ds). If you haven't
got the premises, you can't conclude the conclusion.
In particular, suppose I have a cart. I push it forward across the
table. I feel resistance, a force F. I move it a distance ds. When I let
go, it comes to rest promptly. Can you conclude that non-conservative
forces are at work? No. The cart I had in mind has some clockworks
attached to the wheels. When you push it along it winds up the spring
(using purely conservative forces). When I let go the spring doesn't
unwind because of a ratchet. Every wind-up clock in the world works this
way. With a little more complexity I can arrange it so the spring winds up
(always up) whether you push the cart forward or backwards.
Bottom line: Deriving thermodynamics in terms of "work" is a bad
idea. Exhibiting a large pile of books that do it this way isn't going to
make it a good idea.
Thermodynamics is about entropy. Introducing thermodynamics without
talking about entropy is like selling dehydrated water.