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

 1 : jj 143 ##DESCRIPTION 2 : ##Problem 9, section 2.5 Fundamentals of Complex Analysis for Mathematics, 3 : ##Science, and Engineering by E.B. Saff and A.D. Snider 4 : ##ENDDESCRIPTION 5 : 6 : 7 : DOCUMENT(); # This should be the first executable line in the problem. 8 : 9 : loadMacros( 10 : "PG.pl", 11 : "PGbasicmacros.pl", 12 : "PGchoicemacros.pl", 13 : "PGanswermacros.pl", 14 : "PGauxiliaryFunctions.pl" 15 : ); 16 : 17 : $a = non_zero_random( -5, 5, 1 ); 18 :$b = $a + 2; 19 :$c = $a + 4; 20 : 21 : 22 : BEGIN_TEXT 23 : Find a function $$\phi ( x, y )$$ that is harmonic in the region of the first quadrant between the 24 : curves $$xy\ =\ 2$$ and $$xy\ =\ 4$$ and takes on the values $$b$$ on the lower edge and the value 25 : $$c$$ on the upper edge.[Hint: Begin by considering $$z^2$$.]$PAR 26 : \{ans_rule(20)\} 27 : END_TEXT 28 : 29 : $ans = "x*y+$a"; 30 : ANS(fun_cmp( \$ans, var => [ 'x', 'y', 'a', 'i' ] )); 31 : 32 : ENDDOCUMENT(); # This should be the last executable line in the problem.