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| 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. |
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