View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers2AnalyticFunctions/ur_cn_2_2.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('Complex Variables')
   10 ## DBsection('Complex Analytic Functions')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('Complex Analysis')
   15 ## EditionText1('3')
   16 ## AuthorText1('Saff, Snyder')
   17 ## Section1('2.1')
   18 ## Problem1('')
   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 "PGcomplexmacros.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 
   33 $a = non_zero_random( -5, 5, 1);
   34 
   35 $b = random(2,5,1);
   36 $c = random(1,5,1);
   37 $d = random(1,5,1);
   38 
   39 BEGIN_TEXT
   40 Write each of the following functions in the form \(w\ =\ u(x,y)\ +\ iv(x,y)\) :$PAR
   41 (1) \( g(z)\ =\ \frac{$a}{z}\)$PAR \{ans_rule(20)\} \( +\ i \)\{ans_rule(20)\}$PAR
   42 (2) \( q(z)\ =\ \frac{$b z^2\ +\ $c}{|z\ -\ $d|}\)$PAR\{ans_rule(20)\} \( +\ i \) \{ans_rule(20)\}$PAR
   43 (3) \( G(z)\ =\ e^z\ +\ e^{-z}\)$PAR\{ans_rule(20)\} \( +\ i \)
   44 \{ans_rule(20)\}$PAR
   45 $PAR
   46 END_TEXT
   47 
   48 $ans = "$a*x/(x**2+y**2)";
   49 ANS(fun_cmp( $ans, var => [ 'x', 'y' ] ));
   50 $ans = "-1*$a*y/(x**2+y**2)";
   51 ANS(fun_cmp( $ans, var => [ 'x', 'y' ] ));
   52 $ans = "($b*x**2-$b*y**2+$c)/(sqrt((x-$d)**2+y**2))";
   53 ANS(fun_cmp( $ans, var => [ 'x', 'y' ] ));
   54 $ans = "2*$b*x*y/(sqrt((x-$d)**2+y**2))";
   55 ANS(fun_cmp( $ans, var => [ 'x', 'y' ]));
   56 $ans = '2*cos(y)*cosh(x)';
   57 ANS(fun_cmp( $ans, var => [ 'x', 'y' ] ));
   58 $ans = '2*sin(y)*sinh(x)';
   59 ANS(fun_cmp( $ans, var => [ 'x', 'y' ] ));
   60 
   61 
   62 
   63 ENDDOCUMENT();        # This should be the last executable line in the problem.
   64