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1) The E=m*c^2 formula is likely to be introduced, superficially,
when concepts of mass and energy are discussed in mechanics.
The law that you want to remember is E^2 - p^2 c^2 = m^2 c^4
This was introduced in about the 4th week of that course as
an application of the idea of the invariant length of a 4-vector.
Tangential but important note:
Ludwik makes some important points here about how to handle
the depth versus breadth issue. Students need a certain
amount of breadth. But breadth that is nowhere deep is
not right. The diagram I have in mind is this:
bbbbbbbbbdbdbdbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
bbbbbbbbbdbdbdbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
ddddd
ddddd
ddddd
ddddd
ddddd
ddddd
ddddd
ddddd
where breadth is indicated by "b" and depth (in one or
two topics) is indicated by "d".
This picture is the best possible outcome for a course.
The breadth of background is there ... and the students
see what is involved in thinking deeply about some topic.
In later life, they can do their own deep thinking about
topics that weren't deeply covered in class.
So this is an argument for having a "theme" to the course.
Ludwik is specifically suggesting a nuclear theme, but
that isn't the only choice. You could have a biophysics
theme, or an aerospace transportation theme, or whatever.