View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers2AnalyticFunctions/ur_cn_2_16.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('complex','imaginary','harmonic','conjugate')
    6 ## Tagged by cmd6a 4/20/06
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Appendixes')
   10 ## DBsection('Complex Analytic Functions')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('Fundamentals of Complex Analysis for Mathematics, Science, and Engineering')
   15 ## EditionText1('')
   16 ## AuthorText1('E.B. Saff and A.D. Snider')
   17 ## Section1('2.5')
   18 ## Problem1('9')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 $a = non_zero_random( -5, 5, 1 );
   31 $b = $a + 2;
   32 $c = $a + 4;
   33 
   34 
   35 BEGIN_TEXT
   36 Find a function \( \phi ( x, y ) \) that is harmonic in the region of the first quadrant between the
   37 curves \(xy\ =\ 2\) and \(xy\ =\ 4\) and takes on the values \($b\) on the lower edge and the value
   38 \($c\) on the upper edge.[Hint: Begin by considering \(z^2\).]$PAR
   39 \{ans_rule(20)\}
   40 END_TEXT
   41 
   42 $ans = "x*y+$a";
   43 ANS(fun_cmp( $ans, var => [ 'x', 'y', 'a', 'i' ] ));
   44 
   45 ENDDOCUMENT();        # This should be the last executable line in the problem.