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Thom Jameson wrote:
> Thanks a lot for your reply. Is there a companion that
> I can use to complement Baron. I am having trouble
> following the ideas in Baron on the development of
> Calculus by Newton and Leibnitz.
The book I cited by Carl B. Boyer might be a little
easier to follow. However, I haven't looked at Baron's
book in a while, so I'm not sure about this. I do know
that I've always found it very difficult to read about
the history of various math ideas. Mathematical historians
often don't rephrase things very well in modern language
(in my opinion), and I sometimes find it difficult to
extract from their prose *precisely* _who_ knew _what_
and _when_, or at least a clear distinction of what we
know today about these issues and what we don't know
today about these issues. I know the overall evolution
of ideas is more important, and often many different
people contribute in various ways to something that
was only later recognized as significant by someone,
but honestly, I often feel like I'm pulling teeth
when I go to a history of mathematics text for what
I would consider to be a fairly basic issue. For example,
who was the first to consider the possibility of infinitely
many oscillations in a bounded interval and to what end?
(I think it was Cauchy, 1817 or 1818, and it was small
positive powers of x times sin(1/x) to, I think,
illustrate his definition of continuity.) Another
example: Who/when was the first to consider the
possibility that a derivative might not be continuous,
and who/when actually came up with such an example?
(I don't know about the first question, but I think
Darboux in January 1874, and published in 1875, was
the first to come up with an example, the still
standard (x^2)*sin(1/x) example.)
In your case, I'd strongly advise you to go to a
university library, look up the library call numbers
of the four books I gave earlier (if they have them),
and go to where those books are on the shelves and
look for other books where those are located.
Also, the references given in the paper I cite
in the following post will lead you to quite a few
articles about the development of calculus. If you're
interested, I could perhaps post some of the article
titles listed in that reference, but I can't do this
right now because the paper is at home and I'm not.
http://mathforum.org/kb/message.jspa?messageID=4702130
Dave L. Renfro
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