
02364078
a
2005c.01208
Leipnik, Roy B.
Reid, Troy T.
Multivariable Faa di Bruno formulas.
Bogacki, Przemyslaw (ed.) et al., Proceedings of the 9th annual international conference on technology in collegiate mathematics, ICTCM 9, Reno, NV, USA, November 710, 1996. Norfolk, VA: Old Dominion University, Dept. of Mathematics and Statistics (ISBN 0201343126). Electronic paper (1996).
1996
Norfolk, VA: Old Dominion University, Dept. of Mathematics and Statistics
EN
I65
higherorder chain rule
multivariable calculus
The Bruno product for multiple integer sequences is key to the combinatorial Faa di Bruno formula for the univariate higherorder 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 fourthorder partial derivatives of composite functions. Mistakes and omissions are frequent when the ordinary firstorder chain rule is iteratively applied. (author's abstract) (available under http://archives.math.utk.edu/ICTCM/EP9.html)