$\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} $

Lecture 17, 9/30/2022. This page is for Section 1 only.
ACMS 20550: Applied Mathematics Method I
Instructor: Bei Hu, b1hu@nd.edu, Hurley 174A

  1. Constraint; Lagrange Multipliers
    1. We have leart (a) elimination method; (b) implicit differentiation method;
    2. Lagrange Multiplier method:
      Finding the max/min of $ f(x,y) $ under the constraint $\phi(x,y)=$const.
      is the same as finding max/min of
      $F(x,y) = f(x,y)+\lambda \phi(x,y)$ with $\phi(x,y)=$const.
  2. Endpoint (Boundary poibnt). To find max/min, compare values at all points listed below:
    (a) points where 1st derivatives are zero (horizantal tangent);
    (b) end points;
    (c) corner point(s);