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# View of /trunk/NationalProblemLibrary/272/setStewart16_5/problem_1.pg

Sat Jun 3 14:39:59 2006 UTC (7 years ago) by gage
File size: 2132 byte(s)
 Cleaned problem code using convert-functions.pl


    1 ## DESCRIPTION
2 ##   Compute div and curl
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Vector Fields', 'Curl', 'Div')
6 ## Tagged by nhamblet
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Vector Calculus')
10 ## DBsection('Curl and Divergence')
11 ## Date('')
12 ## Author('')
13 ## Institution('ASU')
14 ## TitleText1('Calculus')
15 ## EditionText1('')
16 ## AuthorText1('Stewart')
17 ## Section1('16.5')
18 ## Problem1('')
19
20 DOCUMENT();
22            "PGbasicmacros.pl",
23            "PGchoicemacros.pl",
25            "PGauxiliaryFunctions.pl",
26            "PGgraphmacros.pl",
27            "Dartmouthmacros.pl");
28
29
30 ## Do NOT show partial correct answers
31 $showPartialCorrectAnswers = 1; 32 33 ## Lots of set up goes here 34$a = random(-9,9,1);
35 $a_yz = clean_scalar_string($a, "yz");
36
37 $b = random(-9,9,1); 38$b_xz = clean_scalar_string($b, "xz"); 39 40$c = random(-9,9,1);
41 $c_xy = clean_scalar_string($c, "xy");
42
43 $aa = random(-9,9,1); 44$aa_x2 = clean_scalar_string($aa, "x^2"); 45 46$bb = random(-9,9,1);
47 $bb_xpy2 = clean_scalar_string($bb, "(x+y)^2");
48
49 $cc = random(-9,9,1); 50$cc_xpypz2 = clean_scalar_string($cc, "(x+y+z)^2"); 51 52 ## Ok, we are ready to begin the problem... 53 ## 54 TEXT(beginproblem()); 55 56 57 BEGIN_TEXT 58$BR A) $BR 59 Consider the vector field 60 $$F(x,y,z) = (a_yz, b_xz, c_xy)$$. 61$BR
62 Find the divergence and curl of $$F$$.
63 $BR 64 $$\textrm{div}(F) = \nabla \cdot F =$$ \{ans_rule(20)\}. 65$BR
66 $$\textrm{curl}(F) = \nabla \times F = ($$
67 \{ans_rule(20)\}, \{ans_rule(20)\},\{ans_rule(20)\}$$)$$.
68
69 $PAR 70$BR B) $BR 71 Consider the vector field 72 $$F(x,y,z) = (aa_x2, bb_xpy2, cc_xpypz2)$$. 73$BR
74 Find the divergence and curl of $$F$$.
75 $BR 76 $$\textrm{div}(F) = \nabla \cdot F =$$ \{ans_rule(20)\}. 77$BR
78 $$\textrm{curl}(F) = \nabla \times F = ($$
79 \{ans_rule(20)\}, \{ans_rule(20)\},\{ans_rule(20)\}$$)$$.
80
81 END_TEXT
82
83 ANS(num_cmp(0));
84 ANS(fun_cmp("($c -$b)*x", vars=>3));
85 ANS(fun_cmp("($a -$c)*y", vars=>3));
86 ANS(fun_cmp("($b -$a)*z", vars=>3));
87
88 ANS(fun_cmp("2*$aa*x + 2*$bb*(x+y) + 2*$cc*(x+y+z)", vars=>3)); 89 ANS(fun_cmp("2*$cc*(x+y+z)", vars=>3));
90 ANS(fun_cmp("-2*$cc*(x+y+z)", vars=>3)); 91 ANS(fun_cmp("2*$bb*(x+y)", vars=>3));
92 ENDDOCUMENT();
93
94
95
96


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