[npl] / trunk / NationalProblemLibrary / Rochester / setComplexNumbers2AnalyticFunctions / ur_cn_2_2.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers2AnalyticFunctions/ur_cn_2_2.pg

Tue Jul 17 13:55:24 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1677 byte(s)
Fixed edition tags.


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