Lecture 13, 9/21/2022. This page is for Section 1 only.
ACMS 20550: Applied Mathematics Method I
Instructor: Bei Hu, b1hu@nd.edu, Hurley 174A
Partial Derivatives
$\fcolorbox{white}{yellow}{Keep all other variable fixed while taking derivative} $, e.g., $\frac{\p z}{\p x}, \frac{\p^2 z}{\p x\p y}$.
Notation: $\Big(\frac{\p z}{\p r}\Big)_x$ means taking derivatives with respect to $r$ while keeping $x$ fixed.
Steps:
(a) $\fcolorbox{white}{yellow}{Wirte $z$ as a function of $x$ and $r$,}$ (b) differentiate
Taylor series
$ f(x,y) = \sum_{n=0}^\infty \frac1{n!} \Big( h \frac{\p}{\p x}+ k \frac{\p}{\p y}\Big)^n f(a,b), \mm h =x-a, \m h= y-b$.