View of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/17_Fundamental_Theorems_of_Vector_Analysis/17.3_Divergence_Theorem/17.3.3.pg

    1 ## DBsubject('Calculus')
    2 ## DBchapter('Fundamental Theorems of Vector Analysis')
    3 ## DBsection('Divergence Theorem')
    4 ## KEYWORDS('calculus')
    5 ## TitleText1('Calculus: Early Transcendentals')
    6 ## EditionText1('2')
    7 ## AuthorText1('Rogawski')
    8 ## Section1('17.3')
    9 ## Problem1('3')
   10 ## Author('JustAsk - Kobi Fonarov')
   11 ## Institution('W.H.Freeman')
   12 
   13 DOCUMENT();
   14 
   15 loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl");
   16 loadMacros("Parser.pl");
   17 loadMacros("freemanMacros.pl");
   18 loadMacros("PGauxiliaryFunctions.pl");
   19 loadMacros("PGgraphmacros.pl");
   20 loadMacros("PGchoicemacros.pl");
   21 
   22 TEXT(beginproblem());
   23 
   24 $context = Context();
   25 $context->variables->add(y=>'Real');
   26 $context->variables->add(z=>'Real');
   27 
   28 $a=random(1,9);
   29 $b=random(1,9);
   30 $c=random(1,9);
   31 $d=random(1,9);
   32 
   33 $fi=Formula("$a*x-2*z*x^{$b}")->reduce();
   34 $fj=Formula("$c*z-x*y")->reduce();
   35 $fk=Formula("z^{$d}*x^2")->reduce();
   36 
   37 $fitag=Formula("$a-$b*2*z*x^{$b-1}")->reduce();
   38 $fjtag=Formula("-x")->reduce();
   39 $fktag=Formula("$d*z^{$d-1}*x^2")->reduce();
   40 
   41 $answer=Formula("$fitag+$fjtag+$fktag")->reduce();
   42 
   43 $curve="\mathcal{C}";
   44 $domain="\mathcal{D}";
   45 $surf="\mathcal{S}";
   46 $FF="\mathbf{F}";
   47 $curl="\text{curl}";
   48 $ii="\mathbf{i}";
   49 $jj="\mathbf{j}";
   50 $kk="\mathbf{k}";
   51 $dive="\text{div}";
   52 Context()->texStrings;
   53 
   54 BEGIN_TEXT
   55 \{ textbook_ref_exact("Rogawski ET 2e", "17.3","3") \}
   56 $PAR
   57 Compute the divergence of the vector field: $PAR
   58 \[$FF = \left< $fi,$fj,$fk\right>\]
   59 \($dive ($FF) = \) \{ans_rule()\} $PAR
   60 $PAR
   61 
   62 END_TEXT
   63 
   64 ANS($answer->cmp);
   65 
   66 Context()->texStrings;
   67 SOLUTION(EV3(<<'END_SOLUTION'));
   68 $PAR
   69 $SOL $PAR
   70 \[$dive ($FF) =\frac{\partial }{\partial x}($fi)+\frac{\partial }{\partial y}($fj)+\frac{\partial }{\partial z}($fk)=
   71 \]\[($fitag)+($fjtag)+($fktag)=$answer
   72 \]
   73 END_SOLUTION
   74 
   75 ENDDOCUMENT();