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  \textbf{Math 436, Fall 2000\\
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   Homework}
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 Assignment 1, due Wednesday, August 30

\noindent
p.\ 2, \#2,4,5

\noindent
p.\ 4, \#2  (Note: The function should be
\begin{math}
  u(x,y)=e^{kx}e^{k^2y}.
\end{math})

\noindent
p.\ 9 \#1,3 (Note: In \#1, the last condition should be
\begin{math}
  u_x(L;t)=0.
\end{math}
In \#3, the last term in the last condition should be
\begin{math}
  u(L;t).
\end{math})


\noindent
p.\ 10 \#1-4

\noindent
p.\ 13 \#2,3

\noindent
p.\ 17 \#1,3

\noindent
p.\ 21 \#4

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Assignment 2, Due Wednesday, September 6

p.\ 33 \#3,5,8,10,15

p.\ 486 \#4,5,6,8,9a,b,11a,b,12,14,15


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Assignment 3, Due Wednesday, September 13


p.\ 486 \#4,5,6,8,9a,b,11a,b,12,14,15

p.\ 476 \#1,6,8,12,16,33

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Assignment 4, Due Wednesday, September 20


p.\ 44 \#1,5,16a,f,17a,f,32,33

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Assignment 5, Due Wednesday, September 27


p.\ 54 \#1,2,4,9,10,15,17,21,22

Also, graph $D_N$, $N=5,10,\dots,50$ by computer.


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Assignment 6, Due Wednesday, October 4


p.\ 69 \#4,5,6,9,10,11,14

p.\ 75 \#1-3,7,8,11,12 (Note: There's a typo in \#11(b).  It
should be
\begin{displaymath}
  -\phi(N)\le \sum _{N+1}^\infty \phi (n) -\int _N^\infty \phi(x)\,dx.
\end{displaymath}
As a result, the left side in \#12(a) should be 
\begin{math}
  \frac {-1}{N^s}.
\end{math})

p.\ 83 \#3-5

Graph the partial sum
\begin{math}
 f_{2N-1}
\end{math}
of the Fourier series of the function
\begin{eqnarray*}
  f(x)=\left\{
      \begin{array}{rl}
       1 & x\in (0,\pi]\\
      -1 & x\in [-\pi,0)
      \end{array} \right.
\end{eqnarray*}
for
\begin{math}
  N=10,50,
\end{math}
and one significantly larger value.

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Assignment 7, Due Wednesday, October 11


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p.\ 108 \#3,7,10,12,13,15,17,21

Although these problems won't be due until after the midterm, some of
them are a good reminder of some of the material in Chapter 0.



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Assignment 8, Due Wednesday, October 25


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p.\ 120 \#1,3,5-9,12,14


p. 133 \#1,3,4,11

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Assignment 9, Due Wednesday, November 1


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p. 150 \#1,2,5,6,11,13,17,18

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Assignment 10, Due Wednesday, November 8


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p.\ 168 \#1,3,4,7,9,13-15



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Assignment 11, Due Wednesday, November 15



\medskip
p.\ 181 \#13,15,16,18,24

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\noindent Use Maple, Mathematica, or Matlab
 to graph the Poisson kernel for the unit disk
(i.e.,  $R=1\/$) with  $r=.5,\ r=.9,\  r=.99 \mbox{ and }r= .999\/$.
Make sure that your graphs are reasonable.

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Here is a tentative list of the remaining assignments.

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Assignment 12, Due Wednesday, November 22

p. 292 \#5,7,13,16,19

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Assignment 13, Due Wednesday, December 6

p. 308 \#6,7,8,15,17


\medskip

\noindent
Use Maple, Mathematica or Matlab
 to graph the Gauss-Weierstrass kernel with  $K=1\/$
for  $t=10,\ t=1, \ t=.1,\ t=.01,\ t=.001, \ t=.0001, \ t=.00001,
t=.000001, \ t=.0000001\/$.  Make sure that your graphs are
reasonable.



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