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

Fri Apr 28 13:46:21 2006 UTC (7 years ago) by jjholt
File size: 1187 byte(s)
Added tags.  --JH


    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
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.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.