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<15> Sun Dec  9 11:39:41 MST 2007
Final set, problem 3. 
I left out the boundary condition:
u(0,y) = 0, 0 <= y <= 1.
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<14> Fri Dec  7 10:39:40 MST 2007
Hint for problem 3: there are four
independent combinations formed by the general -r and -theta solutions you
ought to have found  -- what are they for n=0?
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<13> Sun Nov 25 00:32:54 MST 2007
In problem 1a, set 9: the period for the case of a Fourier series should be 2
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<12> Tue Nov 13 11:37:30 MST 2007
more typos on set 8:
eq. in problem 1 fixed
second recurrence in problem 5 fixed
(please see set 8 posted with corrections)
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<11> Wed Nov  7 23:48:13 MST 2007
There were typos in Set 8, problem 4: 
in the first recurrence relation the "z" should have been "2"; 
in the second recurrence relation the "z" should not be there; 
these are now corrected. Also, hints were added for problems 5 and 6. 
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<10> Tue Nov  6 11:10:29 PST 2007
I seem to have posted the wrong solution for set 6, problem 5 (Abel's
equ.), and it may have confused our grader. I will post the correct version
online asap-you may want to take a close look and ask me to redress any 
complaints!
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<9> Thu Oct 25 13:26:41 MDT 2007
The problem on Abel's equation (set 6) is discussed in the text. 
Also, the due date on set 6, set 7 has been moved up by 4 days
to the following Tuesday.
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<8> Wed Oct 24 22:27:36 MDT 2007
Problem 2 on set 6 requires special consideration for $\nu >0$, because
the contour integral inversion formula can only be used effectively when
$-1 < \nu <0$. I will post some notes on how this can be treated, and also
discuss it briefly in class on Thursday (I re-posted hw. 6 with a couple of
hints on the class page).
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<7> Wed Oct 24 22:27:36 MDT 2007
There was an error in the solutions for set 5, problem 3b; the correct 
answer is (latex notation) $I = -\frac{\sqrt{3}\pi}{9}$.
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<6> Sun Oct 14 20:02:51 MDT 2007
The due date of the take-home exam 1 is in class this coming Tuesday.
If for any reason you cannot make it I will accept exams until 12:15,
ie. the end of Tuesday's office hour.
 Hope to see you all on Tuesday!
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<5> Sat Sep 29 06:58:03 MDT 2007
 Hw 5 was posted on ereserves; it is also on the class web page now
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<4> Sun Sep  9 18:44:39 MDT 2007
The wronski formula for b1: b1 = -a1/a0^2
(was mistyped; has been fixed in the posted homework 3)
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<3> Wed Sep  5 00:14:39 MDT 2007
Hints for hwk. 2
Problem (6c): here the integrand is the product of two functions; you
 need to decide whether f(z) is analytic inside the unit circle. As we 
 discussed in class yesterday, a uniformly convergent series can be integrated
 term-by-term. What is the radius of convergence of the series representing f(z)?
Problem (6d): like in part c, if the series is uniformly convergent
 you can integrate term-by-term. Of course the integrals involving
 analytic functions will vanish, while those involving an analytic
 function over a power of z can be computed using Cauchy's formula.
Problem (8): here try a simple example, like
 P(z) = (z-1)(z-2)(z-3) and make sure you see why
 P'(z)/P(z) = 1/(z-1) + 1/(z-2) + 1/(z-3)
 and why Cauchy's formula gives for the integral of P'(z)/P(z) around 
 a contour enclosing all three singular points the value 2 pi i * 3. 
 Then you can see by analogy how the general case works.
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<2> Tue Sep  4 12:14:44 MDT 2007
note there were some typos and omissions in set 2, that have now been fixed.
(factor of 2 pi i in last problem, definition of contour in problem 1c)
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NOTE: you must also email me a 4 (alphanumeric) digit pin so you
can check your grades when I begin posting them (do not use any
string from your SSN!) 

(I will maintain a news page, where I will try to answer your 
questions that might be of interest to the rest of the class
---all identifying info will be removed)
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<1> Please send me email with your name, major, and a list of all
math courses w. dates when you took them. I also would like a list
of all your engineering/physics or other courses of technical content,
again with dates. It would help me to teach a better class if you also
include with each math course a list of subsequent courses for which
it was useful (if none, then list nothing!). 
 If you have some comments about the class policy I would like to know
them too!
   My email is:      vageli@math.unm.edu
Thanks,
  Vageli
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