differential propositional calculus : appendix 3

(Application)

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

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 x + d y

d y

d x + d y

d x

d x + d y

d y

d x

f₃

f₁₂

d x

f₆

f₉

d x + d y

f₅

f₁₀

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 y

d x

d y

d x + d y

d x

d x + d y

d y

d x

d y

d x + d y

f₁₅

0.2 Partial Differentials and Relative Differentials

Partial Differentials and Relative Differentials

d f =

∂_xf ⋅ d x + ∂_yf ⋅ d y

f₀

( )

f₁

f₂

f₄

f₈

(x)(y)

(x) y

x (y)

x y

(y)

(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)

d x

f₆

f₉

(x, y)

((x, y))

d x + d y

f₅

f₁₀

(y)

d y

f₇

f₁₁

f₁₃

f₁₄

(x y)

(x (y))

((x) y)

((x)(y))

(y)

(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

(( ))

"differential propositional calculus : appendix 3" is owned by Jon Awbrey.
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differential propositional calculus : appendix 3

Contents

0.1 Taylor Series Expansion

0.2 Partial Differentials and Relative Differentials

Pending Errata and Addenda

Discussion

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