id: 02364078
dt: a
an: 2005c.01208
au: Leipnik, Roy B.; Reid, Troy T.
ti: Multivariable Faa di Bruno formulas.
so: Bogacki, Przemyslaw (ed.) et al., Proceedings of the 9th annual
international conference on technology in collegiate mathematics, ICTCM
9, Reno, NV, USA, November 7‒10, 1996. Norfolk, VA: Old Dominion
University, Dept. of Mathematics and Statistics (ISBN 0-201-34312-6).
Electronic paper (1996).
py: 1996
pu: Norfolk, VA: Old Dominion University, Dept. of Mathematics and Statistics
la: EN
cc: I65
ut: higher-order chain rule; multivariable calculus
ci:
li:
ab: The Bruno product for multiple integer sequences is key to the
combinatorial Faa di Bruno formula for the univariate higher-order
chain rule derived in 1850 (It can be found in some European calculus
text books). This extremely useful formula (in statistics and physics)
is normally restricted to derivatives of order four. For multivariate
statistics and solid (or fluid) mechanics, composite derivative
problems in two, three, or four variables are quite normal, and
sometimes appear in undergraduate contexts. Master’s degree students
are often exposed to multivariable problems involving second, third, or
even fourth-order partial derivatives of composite functions. Mistakes
and omissions are frequent when the ordinary first-order chain rule is
iteratively applied. (author’s abstract) (available under
http://archives.math.utk.edu/ICTCM/EP-9.html)
rv: