negative "R" Subscript, "a" "d" "i" "u" "s" , Baseline−Radius
"R" Subscript, "a" "d" "i" "u" "s" , BaselineRadius
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Calculations
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"f" left parenthesis, "x" , "y" , right parenthesisfx,y
"f" left parenthesis, "x" Subscript, 00 , Baseline , "y" Subscript, 00 , Baseline , right parenthesisfx00,y00
r1c1:
r1c2: 0.8 4 1 4 7 0 9 80.84147098
r1c3:
r2c1:
r2c2:
r2c3:
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"Q" left parenthesis, "x" , "y" , right parenthesisQx,y
"Q" left parenthesis, "x" Subscript, 00 , Baseline , "y" Subscript, 00 , Baseline , right parenthesisQx00,y00
r1c1:
r1c2: 1.0 9 1 6 4 0 31.0916403
r1c3:
r2c1:
r2c2:
r2c3:
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"E" "r" "r" "o" "r"Error
"E" Subscript, "r" "r" "o" "r" , Baseline left parenthesis, "x" Subscript, 00 , Baseline , "y" Subscript, 00 , Baseline , right parenthesisErrorx00,y00
r1c1:
r1c2: 29.7 2 9 9 9 529.729995
r1c3:
r2c1:
r2c2:
r2c3:
28
Quaternary Input (Approximation Points)
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29
"x" Subscript, 000 , Baselinex000
"y" Subscript, 000 , Baseliney000
"f" left parenthesis, "x" Subscript, 000 , Baseline , "y" Subscript, 000 , Baseline , right parenthesisfx000,y000
"Q" left parenthesis, "x" Subscript, 000 , Baseline , "y" Subscript, 000 , Baseline , right parenthesisQx000,y000
"E" Subscript, "r" "r" "o" "r" , Baseline left parenthesis, "x" Subscript, 000 , Baseline , "y" Subscript, 000 , Baseline , right parenthesisErrorx000,y000
negative 2−2
2.12.1
r1c3: 0.4 5 9 0 5 5 2 60.45905526
r1c4: negative 1.7 8 9 0 7 8 6−1.7890786
r1c5: 489.7 3 0 5 5489.73055
r1c6:
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negative 3−3
r2c3: 0.7 4 9 2 2 8 7 90.74922879
r2c4: 4.6 9 5 1 3 84.695138
r2c5: 526.6 6 2 7 8526.66278
r2c6:
r3c3:
r3c4:
r3c5:
r3c6:
30
Formulas
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31
Uttryck 32: StartFraction, ∂ squared "f" Over ∂ "x" squared , EndFraction left parenthesis, "x" , "y" , right parenthesis equals "f" Subscript, "x" "x" , Baseline left parenthesis, "x" , "y" , right parenthesis∂2f∂x2x,y=fxxx,y
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Uttryck 33: StartFraction, ∂ squared "f" Over ∂ "y" ∂ "x" , EndFraction left parenthesis, "x" , "y" , right parenthesis equals "f" Subscript, "x" "y" , Baseline left parenthesis, "x" , "y" , right parenthesis∂2f∂y∂xx,y=fxyx,y
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Uttryck 34: StartFraction, ∂ squared "f" Over ∂ "x" ∂ "y" , EndFraction left parenthesis, "x" , "y" , right parenthesis equals "f" Subscript, "y" "x" , Baseline left parenthesis, "x" , "y" , right parenthesis∂2f∂x∂yx,y=fyxx,y
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Uttryck 35: StartFraction, ∂ squared "f" Over ∂ "y" squared , EndFraction left parenthesis, "x" , "y" , right parenthesis equals "f" Subscript, "y" "y" , Baseline left parenthesis, "x" , "y" , right parenthesis∂2f∂y2x,y=fyyx,y
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Uttryck 36: "Q" left parenthesis, "x" , "y" , right parenthesis equals "f" left parenthesis, "x" Subscript, 0 , Baseline , "y" Subscript, 0 , Baseline , right parenthesis positive "f" Subscript, "x" , Baseline left parenthesis, "x" Subscript, 0 , Baseline , "y" Subscript, 0 , Baseline , right parenthesis left parenthesis, "x" negative "x" Subscript, 0 , Baseline , right parenthesis positive "f" Subscript, "y" , Baseline left parenthesis, "x" Subscript, 0 , Baseline , "y" Subscript, 0 , Baseline , right parenthesis left parenthesis, "y" negative "y" Subscript, 0 , Baseline , right parenthesis positive 1 half "f" Subscript, "x" "x" , Baseline left parenthesis, "x" Subscript, 0 , Baseline , "y" Subscript, 0 , Baseline , right parenthesis left parenthesis, "x" negative "x" Subscript, 0 , Baseline , right parenthesis squared positive "f" Subscript, "x" "y" , Baseline left parenthesis, "x" Subscript, 0 , Baseline , "y" Subscript, 0 , Baseline , right parenthesis left parenthesis, "x" negative "x" Subscript, 0 , Baseline , right parenthesis left parenthesis, "y" negative "y" Subscript, 0 , Baseline , right parenthesis positive 1 half "f" Subscript, "y" "y" , Baseline left parenthesis, "x" Subscript, 0 , Baseline , "y" Subscript, 0 , Baseline , right parenthesis left parenthesis, "y" negative "y" Subscript, 0 , Baseline , right parenthesis squaredQx,y=fx0,y0+fxx0,y0x−x0+fyx0,y0y−y0+12fxxx0,y0x−x02+fxyx0,y0x−x0y−y0+12fyyx0,y0y−y02
36
Perspective View
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37
Uttryck 38: theta Subscript, "h" "o" "r" "i" "z" "o" "n" "t" "a" "l" , Baseline equals negative 0.5θhorizontal=−0.5
