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

    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();
   21 loadMacros("PG.pl",
   22            "PGbasicmacros.pl",
   23            "PGchoicemacros.pl",
   24            "PGanswermacros.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