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[parent] differential propositional calculus : appendix 3 (Application)

Contents

  0.1 Taylor Series Expansion
  0.2 Partial Differentials and Relative Differentials

0.1 Taylor Series Expansion

Taylor series Expansion D f = d f + d 2f
d f =
∂xf ⋅ d x  +  ∂yf ⋅ d y
d 2f =
∂xyf ⋅ d x d y
d f|x y d f|x (y) d f|(x) y d f|(x)(y)
f0 0 0 0 0 0 0
f1
f2
f4
f8
(y)
d x
+
(x)
d y
y
d x
+
(x)
d y
(y)
d x
+
x
d y
y
d x
+
x
d y
d x  d y
d x  d y
d x  d y
d x  d y
0
d x
d y
d x + d y
d x
0
d x + d y
d y
d y
d x + d y
0
d x
d x + d y
d y
d x
0
f3
f12
d x
d x
0
0
d x
d x
d x
d x
d x
d x
d x
d x
f6
f9
d x + d y
d x + d y
0
0
d x + d y
d x + d y
d x + d y
d x + d y
d x + d y
d x + d y
d x + d y
d x + d y
f5
f10
d y
d y
0
0
d y
d y
d y
d y
d y
d y
d y
d y
f7
f11
f13
f14
y
d x
+
x
d y
(y)
d x
+
x
d y
y
d x
+
(x)
d y
(y)
d x
+
(x)
d y
d x  d y
d x  d y
d x  d y
d x  d y
d x + d y
d y
d x
0
d y
d x + d y
0
d x
d x
0
d x + d y
d y
0
d x
d y
d x + d y
f15 0 0 0 0 0 0

0.2 Partial Differentials and Relative Differentials

Partial Differentials and Relative Differentials
f ∂f ∂x ∂f ∂y
d f =
∂xf ⋅ d x  +  ∂yf ⋅ d y
f f
f0 ( ) 0 0 0 0 0
f1
f2
f4
f8
(x)(y)
(x) y
x (y)
x  y
(y)
y
(y)
y
(x)
(x)
x
x
(y)
d x
+
(x)
d y
y
d x
+
(x)
d y
(y)
d x
+
x
d y
y
d x
+
x
d y
 
 
 
 
 
 
 
 
f3
f12
(x)
x
1
1
0
0
d x
d x
 
 
 
 
f6
f9
(x, y)
((x, y))
1
1
1
1
d x + d y
d x + d y
 
 
 
 
f5
f10
(y)
y
0
0
1
1
d y
d y
 
 
 
 
f7
f11
f13
f14
(x  y)
(x (y))
((x) y)
((x)(y))
y
(y)
y
(y)
x
x
(x)
(x)
y
d x
+
x
d y
(y)
d x
+
x
d y
y
d x
+
(x)
d y
(y)
d x
+
(x)
d y
 
 
 
 
 
 
 
 
f15 (( )) 0 0 0 0 0

"differential propositional calculus : appendix 3" is owned by Jon Awbrey.
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See Also: differential logic, minimal negation operator


This object's parent.

Cross-references: Taylor series

This is version 1 of differential propositional calculus : appendix 3, born on 2009-05-25.
Object id is 780, canonical name is DifferentialPropositionalCalculusAppendix3.
Accessed 2165 times total.

Classification:
Physics Classification: 02. (Mathematical methods in physics)
 02.10.Ab (Logic and set theory)
 02.10.Ox (Combinatorics; graph theory)
 02.10.Ud (Linear algebra)
 02.20.-a (Group theory )
 02.30.-f (Function theory, analysis)
 02.40.-k (Geometry, differential geometry, and topology )
 02.40.Yy (Geometric mechanics )
 02.50.Tt (Inference methods)
 02.70.-c (Computational techniques )
 02.70.Bf (Finite-difference methods)
 02.70.Wz (Symbolic computation )
Pending Errata and Addenda
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