$\newcommand{\dis}{\displaystyle} \newcommand{\m}{\hspace{1em}} \newcommand{\mm}{\hspace{2em}} \newcommand{\x}{\vspace*{1ex}} \newcommand{\xx}{\vspace*{2ex}} \let\limm\lim \renewcommand{\lim}{\dis\limm} \let\fracc\frac \renewcommand{\frac}{\dis\fracc} \let\summ\sum \renewcommand{\sum}{\dis\summ} \let\intt\int \renewcommand{\int}{\dis\intt} \newcommand{\sech}{\text{sech}} \newcommand{\csch}{\text{csch}} \newcommand{\Ln}{\text{Ln}} \newcommand{\p}{\partial} \newcommand{\intd}[1]{\int\hspace{-0.7em}\int\limits_{\hspace{-0.7em}{#1}}} $

Lecture 25, 10/25/2021. This page is for Section 1 only.
ACMS 20550: Applied Mathematics Method I
Instructor: Bei Hu, b1hu@nd.edu, Hurley 174A

  1. Surface Area $z =f(x,y)$:
    $ \intd{} dA = \intd{} \sec \gamma \; dxdy \mm $ where $\m \sec\gamma = \sqrt{1+\Big(\frac{\p f}{\p x}\Big)^2++\Big(\frac{\p f}{\p y}\Big)^2 }$


    Normal vector $\vec n = \frac{\nabla \Phi}{|\nabla \Phi|}$, where the surface is given by $\Phi(x,y,z)=$constant.

    Using appropriate coodinate system is crucial.