Expression 33: "s" Subscript, "s" , Baseline left parenthesis, "t" , right parenthesis equals "t" squared left parenthesis, 3 minus 2 "t" , right parenthesissst=t23−2t
33
Expression 34: "h" Subscript, "s" , Baseline left parenthesis, "x" , right parenthesis equals "f" Subscript, "r" , Baseline left parenthesis, 43758.5 4 5 3sin left parenthesis, 12.9 8 9 8 "x" plus 12.8 7 , right parenthesis , right parenthesishsx=fr43758.5453sin12.9898x+12.87
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Expression 35: "H" Subscript, "s" , Baseline left parenthesis, "x" , "y" , right parenthesis equals "f" Subscript, "r" , Baseline left parenthesis, 23892.5 8sin ( 28.2 8 "x" plus 73.7 "y" ) , right parenthesisHsx,y=fr23892.58sin(28.28x+73.7y)
35
These functions/variables are used for visualizing explicit surface
36
Expression 37: "N" equals 30N=30
88
3030
37
Expression 38: "R" equals 4 fifths "S"R=45S
equals=
88
38
Expression 39: "q" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis equals StartFraction, "R" Over "N" , EndFraction floor left parenthesis, "N" "t" , right parenthesisqet=RNfloorNt
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Expression 40: "r" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis equals "R" left parenthesis, 2 "N" left parenthesis, "t" minus StartFraction, 1 Over "N" , EndFraction floor left parenthesis, "N" "t" , right parenthesis , right parenthesis minus 1 , right parenthesisret=R2Nt−1NfloorNt−1
Expression 54: "F" left parenthesis, "x" , "y" , right parenthesis equals 0.3 Start sum from "k" equals 1 to 3, end sum, 0.5 Superscript, "k" , Baseline exponent left parenthesis, sin left parenthesis, 2 Superscript, "k" , Baseline left parenthesis, "x" plus "H" Subscript, "s" , Baseline left parenthesis, "k" , "k" plus 1 , right parenthesis , right parenthesis plus "k" squared "t" Subscript, "m" , Baseline , right parenthesis cos left parenthesis, 2 Superscript, "k" , Baseline left parenthesis, "y" plus "H" Subscript, "s" , Baseline left parenthesis, 1 minus "k" , "k" , right parenthesis , right parenthesis minus "k" squared "t" Subscript, "m" , Baseline , right parenthesis , right parenthesisFx,y=0.33∑k=10.5kexpsin2kx+Hsk,k+1+k2tmcos2ky+Hs1−k,k−k2tm
54
Expression 55: left parenthesis, "U" left parenthesis, "q" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , "r" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , "F" left parenthesis, "r" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , "q" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , right parenthesis , right parenthesis , "V" left parenthesis, "q" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , "r" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , "F" left parenthesis, "q" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , "r" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , right parenthesis , right parenthesis , right parenthesisUqet,ret,Fret,qet,Vqet,ret,Fqet,ret
domain t Minimum: negative 1−1
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: 1 plus StartFraction, 1 Over "N" , EndFraction1+1N
55
Expression 56: left parenthesis, "U" left parenthesis, "r" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , "q" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , "F" left parenthesis, "r" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , "q" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , right parenthesis , right parenthesis , "V" left parenthesis, "r" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , "q" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , "F" left parenthesis, "r" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , "q" Subscript, "e" , Baseline left parenthesis, "t" , right parenthesis , right parenthesis , right parenthesis , right parenthesisUret,qet,Fret,qet,Vret,qet,Fret,qet
domain t Minimum: negative 1−1
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: 1 plus StartFraction, 1 Over "N" , EndFraction1+1N