- as δ (
x ) = { 0 ,
x ≠ 0 ∞ ,
x = 0 {\displaystyle \
delta (
x)={\begin{cases}0,&
x\neq 0\\{\infty },&
x=0\end{cases}}} such that ∫ − ∞ ∞ δ (
x ) d
x = 1. {\displaystyle...
-
x )
x ⋅ ( − i ℏ d d
x ) ψ (
x ) d
x − ∫ − ∞ ∞ ψ ∗ (
x ) ( − i ℏ d d
x ) ⋅
x ψ (
x ) d
x = i ℏ ⋅ ∫ − ∞ ∞ ψ ∗ (
x ) [ ( −
x ⋅ d ψ (
x ) d
x ) + d (
x ψ...
-
factoring Δ
x {\displaystyle \
Delta x} out:. ∫ a b f (
x ) d
x ≈ Δ
x 2 ( f (
x 0 ) + 2 f (
x 1 ) + 2 f (
x 2 ) + 2 f (
x 3 ) + 2 f (
x 4 ) + ⋯ + 2 f (
x N − 1...
- {\displaystyle \
Delta x'=
x'_{2}-
x'_{1}\ ,\ \
Delta t'=t'_{2}-t'_{1}\ .} Eq. 2: Δ
x =
x 2 −
x 1 , Δ t = t 2 − t 1 . {\displaystyle \
Delta x=
x_{2}-
x_{1}\...
- τ
x y γ
x y = F / A Δ
x / l = F l A Δ
x {\displaystyle G\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\tau _{xy}}{\gamma _{xy}}}={\frac {F/A}{\
Delta x/l}}={\frac...
-
uncertainty principle: Δ
x Δ p ≥ ℏ 2 {\displaystyle \
Delta x\
Delta p\geq {\frac {\hbar }{2}}\;} and Δ
X Δ Y ≥ 1 4 {\displaystyle \;\
Delta X\
Delta Y\geq {\frac {1}{4}}}...
- lim Δ
x → 0 F (
x 1 + Δ
x ) − F (
x 1 ) Δ
x = lim Δ
x → 0 f ( c ) , {\displaystyle \lim _{\
Delta x\to 0}{\frac {F(
x_{1}+\
Delta x)-F(
x_{1})}{\
Delta x}}=\lim...
-
quotient is: Δ f Δ
x (
x + h / 2 ) = f (
x + h ) − f (
x ) h . {\displaystyle {\frac {\
Delta f}{\
Delta x}}(
x+h/2)={\frac {f(
x+h)-f(
x)}{h}}.} If the input...
- x , y ) + I
x (
x , y ) Δ
x + I y (
x , y ) Δ y {\displaystyle I(
x+\
Delta x,y+\
Delta y)\approx I(
x,y)+I_{
x}(
x,y)\
Delta x+I_{y}(
x,y)\
Delta y} This produces...
- rate of heat flow is: Q Δ t = − k A Δ T Δ
x {\displaystyle {\frac {Q}{\
Delta t}}=-kA{\frac {\
Delta T}{\
Delta x}}}
where Q {\displaystyle Q} is the net heat...
