PGdiffeqmacros.pl DESCRIPTION

# Macros for Prills 163 problems

########## # sub addtwo adds two strings formally # An "indicator" for a string is a # number ,e.g. coefficient,which indicates # whether the string is to be # added or is to be regarded as zero. # The non-zero terms are formally added as strings. # The input is an array # (\$1staddend, \$1stindicator,\$2ndaddend,\$2ndindicator) # The return is an array # (formal sum, indicator of formal sum)

######## # sub add generalizes sub addtwo to more addends. # It formally adds the nonzero terms. # The input is an array of even length # consisting of each addend,a string, # followed by its indicator.

diffop(\$a,\$b,\$c)

####### # sub diffop cleans up the typed expression # of a diff. operator. # input @diffop =(\$A,\$B,\$C) is the coefficients. # input is given as arguments viz difftop(\$A,\$B,\$C); # output is the diff. operator as a string \$L in TEX

######## # sub rad simplifies (a/b)*(sqrt(c)) # input is given as arguments on rad viz.: rad(\$a,\$b,\$c); # \$a,\$b,\$c are integers and \$c>=0 and \$b is not zero. # output is an array =(answer as string,new\$a,new\$b, new\$c)

simpleexp(\$r,\$ind)

#### # sub exp simplifies exp(\$r*t) in form for writing perl # or tex. The input is exp(\$r,\$ind); \$ind indicates whether # we want perl or tex mode. \$r is a string that represents # a number. # If \$ind = 0 output is "exp((\$r)*t)", simplified if possible. # If \$ind = 1 output is "exp((\$r)*t)", simplified if possible.

undeterminedSin(\$A,\$B,\$C,\$r,\$w,\$q1,\$q0,\$r1,\$r0)

################# # undeterminedSin is a subroutine to solve # undetermined coefficient problems that have # sines and cosines. # The input is an array (\$A,\$B,\$C,\$r,\$w,\$q1,\$q0,\$r1,\$r0) # given as arguments on undeterminedSin # \$L =\$A y'' + \$B y' + \$C y # \$rhs = (\$q1 t + \$q0) cos(\$w t)exp(\$r t) + # (\$r1 t + \$r0) sin(\$w t)exp(\$r t) # The subroutine uses undetermined coefficients # to find a solution \$y of \$L = \$rhs . # The output \is \$y

``````    rungeKutta4a

Answer checker filter for comparing to an integral curve of a vector field.

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