There is a calculus book in pdf form online at djm.cc. I found this in my search for a reference to Netwton's difference quotient method [wikipedia], which I use in a paper and which Jeff wanted me to put in a reference for.
Looking for a reference to Netwton's difference quotient method was instructive because it led me to a problem I had not had to deal with yet: if you have a numerical method for computing a function f(x) then the simple newton's difference quotient method
d f(x) f(x+h) - f(x)
------ = --------------
dx h
is problematic because for small values of h (as required by the method) f(x+h) is almost the same as f(x) and the difference and the division may lead you into rounding errors.
This paper addresses that issue.
Looking for a reference to Netwton's difference quotient method was instructive because it led me to a problem I had not had to deal with yet: if you have a numerical method for computing a function f(x) then the simple newton's difference quotient method
d f(x) f(x+h) - f(x)
------ = --------------
dx h
is problematic because for small values of h (as required by the method) f(x+h) is almost the same as f(x) and the difference and the division may lead you into rounding errors.
This paper addresses that issue.
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